I have few memories of the Gothic series way back when (mid-2000s) when I first started playing G2...

But I've beaten G1 3 times or so now and I really really like it. Every time I start playing G2 I have SOO much trouble continuing because I hate how the system works compared to G1...

-Minimum damage you take from an attack is 5, instead of 1 (as it was in G1)
-Until you increase your strength (or get a substantially higher damage weapon) you will deal an absolute minimum amount of damage with every swing
-Magic is way harder to get into, as you need to pay LP to learn how to craft a rune for every spell you want to cast
-Spells cost in the multiples of 5 mana, whereas in G1 it was in multiples of 1 mana...
-Base mana potion is 50 mana, whereas in G1 it was 30 (making it much easier to get into the swing of using magic efficiently because you could refill your mana bar without wasting)
-Don't bother trying to hit things at a distance with a bow until your bow skill is seriously high
-EVERYBODY KEEPS STEALING MY KILLS! xO
-It's really easy to take a marginally different route on a task and get a significantly reduced reward...
-Weapon range is weird as hell, my character should have a foot or two feet of distance from an enemy which he covers with a weapon... but he can swing a weapon, miss because he's too far away and then get hit by an enemy WITHOUT a weapon when they don't even move...
-Unlike in G1, you will be surrounded by high level weaponry but be unable to utilize it until you're seriously farther in the game (whereas in G1 you tended to be able to use whatever you came across and could get relatively capable against lower tier enemies)
-Many quests cannot be efficiently solved around the time you receive them, and are certainly meant to be taken on later
-In G1 people were about as strong as was logical, and if you were fairly strong you could beat them up... in G2 an average villager will crush you.
-Where you could complete pretty much all the random missions to pick a community to join in G1, in G2 the mercenaries basically turn you into a punching bag
-You cannot pick a lock without lockpick training
-There are now a multitude of hunting skills, almost all are more expensive to learn and far less useful than in G1
-I cannot see ANYTHING with these trees around...

It is simply AGONIZING for me presently...

Can someone tell me if I need to get past the beginning portion of the Valley of Mines before my character starts becoming capable? I'm seriously tired of every single encounter being a huge pain...

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Should I be approaching this with a different mindset? Am I expecting to be able to do too much? I just feel totally incapable playing this game compared to the first...

I don't understand what you're asking.

But if you refer to the how to get to the castle with most benefit when you return to the Valley of Mines, I can only say this:

- walk down the path and talk to the guy that warns you about the orcs (can't remember his name)
- turn left, and walk alongside the river towards orc barricade (in the direction where swamp camp was)
- when you get int he place where the edge of the forest was in G1 you can make a run for it to the castle (not good) or:
* drink a Speed Potion
* have a Fire Rain scroll ready
* gather all the orcs (or as many as possible) by running in the opposite direction and waiting for all to gather and run after you
* when you to the back of the castle, climb that fallen tree trunk, wait for orcs to gather (they won't climb the trunk) and use the scroll - the only orcs that will remain standing will be elites
* that's about 2 -3 - 4 free levels depending on your own level when you get there

If you mean a general advice:
- stick to one fighting style (one-hander / two-hander / bow / crossbow)
- manage carefully your LPs (don't put in DEX and STR / etc - only STR or DEX or ...), because the LP cost of skills increases sky high later on:
1 -30 = 1 LP per 1 skill point
30 to 31 = 2 LP per 1 skill point
60 to 61 = 3 LP per 1 skill point
90 to 91 = 4 LP per 1 skill point
120 to 121 = 5 LP per 1 skill point
- that is why learning how to create potions with permanent effect becomes imperative
- you should use these potions after what you get at least 90 in a stat with normal training
- same goes for tablets - it is imperative to learn to read all of them:
* for a total cost of 30 LP to learn them you will get:

[updated to correct numbers - thanks to 19Uhr30]
+22 strength
+24 dexterity
+42 mana
+205 life energy
+24% one-hander
+20% two-hander
+30% bow
+20% crossbow

...and no way you can get these cheaper than that.

- also don't forget you can pray to shrines (through donations) for extra bonuses
- etc etc

You have to understand that G2 NotR was made this difficult because Gothic fans complained too much about how easy G2 vanilla was (and they are right!), and still you'll find people who claim even NotR is not as hard as they expected.

Hope this gives you an idea.

In II, you are half dead at the beginning - very, very weak.

I just transform into a wolf (orcs don't attack them or the orc dogs (wargs)), run up to the former old camp, untransform, and climb the siege equipment to get in (which, mysteriously, orcs are incapable of climbing and nobody in the castle shoots at them when they are at its base well within crossbow range).

Funnily enough, pretty much the opposite. I played Gothic 2 first and found Gothic 1 to be far too easy. I went into it thinking it would be around the difficulty of its sequel, and started focusing my learning points exclusively on my chosen specialisation (archery and hunting). In chapter 2, I was putting down mobs without even batting an eyelid while in Gothic 2 I was still had to be very careful about picking my battles and avoiding tougher or more numerous enemies. By chapter three, I'd maxed out both bow skill and dexterity, had around 8000 ore and a bunch of expensive miscellaneous crap (mostly animal parts from hunting) in my inventory and from then on was able to get the best bow and later on crossbow the chapter had to offer simply by buying it from Cavalorn for a relative pittance.

At this point, the game was simply a cakewalk. While you had to be very careful about where you spent your learning points in Gothic 2, in Gothic 1, you'd find yourself maxing out skills you rarely ever use simply because you're sitting on a massive pile of learning points with nothing better to spend them on. The lack of any challenge, both in combat and good learning point allocation just makes the whole post chapter 1 game very un-engaging and positively dull. The fact hat there's almost no sidequests and only one I can think of that's actually worth doing (that is the minecrawler plate armour) doesn't exactly help matters.

I happen to think that the truth is somewhere in the middle. In G1 you can easily get 100 STR and one handed weapons level 2 in the first chapter. And that is everything you need until very close before the end of the game.
In Gothic 2 it takes a lot longer to get skilled. You have to avoid many more enimies for much longer and have to be much more careful overall. That is more thrilling but also much more frustrating because there are situations you have to deal with by saving and reloading at lot...
And let us not forget that the G2 system leads you to save the bonus items until you have leveled your primare skills high enough and then use them all at once. That means that you will get an enourmous power boost in chapter 3 or 4. And after that everything is kind of easy. I would not call that an ideal gaming expirience either.
The bonus items in general increase the feeling that you are dealing with resource management. I do not neccesarily like that because it makes immersion into the world harder. And that point is what makes G1 stand out to me anyway. I like the setting much better and I like the story and the twists a lot more.

Just a thought but with the original disc version of Gothic II there was an option to change the keyboard to the system used in Gothic I. Have a look in the Options menu and see if that option is there on the GOG game.

As noted above, Gothic II is a hard game in the beginning, but you should find it a very rewarding experience once you down the first road towards the city. I usually go to the farm and gain some experience points doing jobs for the farmer and a small amount of exploring before I enter the city.

I hope you get to enjoy the game.