I seem to getting my ass kicked on a regular basis in I-war. I'm only on the Gatekeeper mission, like the 2nd one in, but the large wave of enemy craft that come in while I'm in defense of the area seems to take me out really quickly. Are there some general combat tips I should be aware of to keep myself alive longer?

I posted this in a different thread but it's worth repeating here...
Use the A and Z buttons to control your speed rather than the throttle. Soften enemies up from a distance using ripple fire missiles before you go in close and attack.
If you're in trouble try to LDS away. You might get inhibited but often you can get enough distance to make some emergency repairs. Sometimes prioritising an LDS repair is the only way to survive.
For Gatekeeper specifically try to stay behind the L-point. You can then blast the enemies as they jump in their most vulnerable area - the engines, where there's a gap in their shields. Also any enemies will have turn around and approach you to attack, bringing them in range of the activated gunstars.
Try to face your enemies, your shields are strongest at the front.

Very useful tips Ravenger. The ripple missile firing tip is extremely useful when you're outnumbered. If it's possible, use it while turning around the swarm of enemies, so that they are 90° on your left or right : this will allow you to use both missile banks while still having a decent protection from your shields.
I'd like to add another tip : when you're very close to your target (say, about 3km away), switching off the auto-aiming for your main cannon might be a good idea. You'll have to aim manually, preferably using the pilot view. This can be a bit tricky, especially since the cannon is mounted pretty far on the side of the ship, inducing a parallax problem. However, the cannon will fire much more rapidly. This will lead to a overheat pretty fast, but if you're accurate enough you'll be able to do some damage before that. When using this method from behind an enemy, where the shields are almost inoperative, you can do some serious damage before your PBC overheats. And when firing from the front, the great number of shots in a short period of time should overload the target's shield, allowing for 1 or 2 shots to reach the hull.
Also, reading the technical part of the manual is useful if you want to coordinate the repairs efficiently. For instance, it's useless to repair your PBC if your energy production line is down : you won't be able to return fire effectively anyway.

If I remember correctly, PBCs were optimal at 3k or lower. I've seen them do "something" up to 6k, but they fall off rapidly.
One of the important things with Gatekeeper is to keep hostiles within range of the gunstars. They fire rapidly enough to punch through LDAs without too much time.
Should you have to use missiles, it might be a good idea to fire a round from your PBC when the missile will impact. This helps increase the chance of the missile doing damage instead of being absorbed by the LDA.
If you are in trouble, and not able to warp out, prioritizing repairs on the LDAs may be a good choice to give you a chance to absorb an extra hit. There are many times while on the engineering screen that everything is getting put back together only to get it knocked offline again by a new shot.
Keep an eye on the target's status. Look for failed systems like the target's Upper LDA (ULD) or Lower LDA (LLD) and try and fire on that target's side. (Without the LDA, shots fired will go to the hull.)
On the defensive side, try and rotate your ship to even out hits across your own LDA(s) yourself. Remember your training? "Two on one, Two on one!" It applies to your systems as well.
Don't forget that you can also prioritize power. If you're really desperate, you can boost power to other systems by holding CTRL, and pressing an arrow key. Up for shields, left for engines, right for weapons. CTRL-Down will equalize the power. Draining power from other systems makes them less effective!
On stationary targets, or "disabled" (in the sense that the target's power, thrusters, and/or main drive is offline), see if you can't manually aim a ripple fire at a target. This helps cut through LDAs better, and can even provide for more devastating damage.
Is your PBC not doing any damage even though it looks like it's hitting the hull? Double-check that you aren't getting a PBC overheat warning. It takes time to charge a damaging shot from the PBC. Even if it's ready to fire, it doesn't mean it'll do damage at the range you are at. I tend to wait 250ms before I fire the next volley when I start getting overheat warnings.
The RING is a very important piece of your power system, and can take a decent amount of time to repair. You may want to consider putting all four crews to work on it at once.
Too much heat (Shown as the "T" bar in the engineering screen) can result in everything being slowed down. PBCs cool more slowly, thrusters (if they are online) will be weaker, repairs can even be slowed down by excess heat. If you find that your heat generation is going up rapidly, you may want to consider prioritizing the waste heat array.
For basic manouvering, remember that the Dreadnaught's belly thrusters are the strongest. When trying to make a turn, make sure you are pulling back on the stick to make it.
If you absolutely need 6DOF (Wikipedia), hit "N" to disable the automatic support. It will allow you to make some interesting manouvers, and should you need to retreat, you may even be able to "reverse" your way out of there without exposing the unprotected engine component. Press "N" again to reinstate normal flight.

I aced the Gatekeeper mission by boosting power to my weapons for the first couple of waves, and staying behind the l-point.
You can easily destroy the first few ships using cannons alone when they're boosted without even moving out of position, saving your missiles for the later waves.
When the big waves come through you have to switch back to balanced power otherwise they'll rip through your shields, but then you should have a full complement of missile to ripple fire at the enemies, making it much easier.

I can't even finish the Advanced Weapons lesson!
I get behind the hulk, rapid fire my PBCs on its engine, but it seems to take almost no damage, and then it also regenerates.
Am I doing something wrong? It helps to use ripple fire against the hunter-seeker mines, but the Hulk seems indestructible.
But is the damage only reduced when you get the warning, or should you still wait some time between volleys if there's no warning?

For the hulk, you'll want to pepper it with missiles as you approach.
From a cold start you can get away with firing as rapidly as you can, but as things heat up, you need to wait just a little bit.

Subtarget the hulks individual systems and take them out individually with missiles too.

I didn't even know the hulk had sub-systems.

Most ships, even the hulk have subsystems. With the larger ships it's often better to take out as many of the individual systems as you can first instead of just pounding at their hull.

I can't find any reference to sub-system targeting in I-War. Manual or otherwise.

It's actually referred to as sub-targeting. See page 100 of the manual:
----------------------
Combat Guide: Targeting individual systems
When fighting large ships, taking out a specific turret or shieldarray
can be a much more effective strategy than simply blasting
away at the ship’s superstructure. Watch for the ship venting
red-gas, this is a clear sign of a major system failing.
To use sub-targeting: designate the ship in the normal way to
make it your target. Then press the targeting key <<T>> or
<<JOY BUTTON 2>> again. Double designating the ship activates
the sub-targeting function. A box cursor will then appear
over the currently sub-targeted system. To target the next system,
press the targeting key again.
------------------------
Subtargeting may only work at medium-close range.
Missiles are a great way to hit sub-targets.

You could always get this:
Prima's Official Strategy Guide to Independence War (Paperback)
http://www.amazon.com/gp/offer-listing/0761518177/ref=sr_1_1_olp?ie=UTF8&amp;s=books&amp;qid=1277727950&amp;sr=1-1&amp;condition=used
Mine comes in handy.

Thanks for all the feedback, I did manage to get through the Gatekeeper mission, my main issue was that when I approached enough baddies they would swarm and kill me very quickly. After a couple more tries I managed to take them out, although it was close as one of them basically crippled me and I had to wait until I finished repairs to take out the last one that was attacking the basestar.

This is also my first time playing I-War and I am having issues with this mission. I have been having more success picking mines off my ship using the weapons view, but with all the contacts on screen i'm finding it difficult to lock on to the hulk once I close the distance in.

Switching to inertial flight mode seems to help so I can strafe the vessel.

Do you guys use the weapons view much during combat? Any tips? Do you usually need to switch back and forth between different views? Use any of the autopilot modes? Instant shields?

I didn't even know that my ship had been armed with missiles at this point in the game so I will give those a shot on my next attempt.

BTW, I think this game is genius. I enjoy the "WWII planes in space" genre quite a bit, but some aspects of certain games there are a bit weird, like speed limits in space!
The realism in this game is really cool, although a bit overwhelming at first. I like how it not only has newtonian physics, but the entire game is designed with a lot of thought and detail to how real space combat might be like. It keeps the realism as well as the fun by retaining a little bit of that "planes in space" feel. Very original.