Because it seems that I've encountered quite a number of buggers who will always interrupt me, no matter which merc I use. Whether it's Ivan or Magic, the 2 fastest mercs in my team, these enemies will always interrupt me whenever I:
a) shoot them
b) walk in their line of sight
c) noise alert them to my presence
How is interruption handled in the game? Does anyone have any ideas on how to take down these guys without getting shot at?

I haven't played JA1 but I would hazard a guess that maybe your team members aren't sneaky enough. Try getting someone who has a high stealth stat/ability and send them out as a scout and try to surprise the enemy that way....

Ah thanks, but there's no stealth stat in JA1 lol. I figured that it's either Dexterity of Agility, but both Ivan and Magic have got it pretty high =\

I never dug into that really deep, but I assume there's a kind of stealth stat.
You can use camouflage and you have an option to sneak around (think it's clicking a place to go while holding down shift).
I hardly ever used Magic in JA1, but I've always used Ivan and he had his share of interupts, both in his favor and against him.
I'm guessing line of sight combined with remaining action points might have something to do with that, but that's just a guess.

Hmm I have to find out how this works. Late game, every single opponent manages to interrupt Ivan and Magic, which is getting to the point of ex-bloody-tremely annoying. I'm still too poor to hire Mike though, so I won't be able to try him out

I'm just shooting in the dark here but from what I've played of the game it seems to work similar to X-com. If an enemy spots one of your characters and has a higher remaining percentage of action points then they interrupt that character. Also hold shift when telling your merc where to go to make them sneak.

It's been a while since I played JA1. But I recall that having a higher level helps you get interupts. (That's how JA2 handles it at least) You could try this out by hiring Pops :-)

It's been a while since I last touched JA. Busy with Freespace atm. I doubt it's got to do with the action points though, since I get spotted even with near full AP. The higher level suggestion sounds plausible. I will try it out when I have time, thanks!

It is the sum of many factors. Using stealth (hold shift while moving) and camouflage decreases the chances, but the real culprits are wisdom (affects also interrupts you get) and level. Some cases it is nearly impossible to go without getting an interrupt on you. This happens most when the opponent is hidin so well that you just can't spot it. Just use alternate routes, supressing fire, explosives or smoke bombs to get through.

The problem is when they're inside the building, their backs turned to you, and when you fire on them, they interrupt my merc, killing him because they have the unfair advantage of almost full AP. It's just so unfair that they can interrupt you once you hit them, because it means your merc has a high chance of dying.
So it's like this: if I send my toughest merc (Magic or Ivan) into the building, shoot the guy once, my merc gets shot thrice. If I wait outside the building to ambush the guy (I don't have stones), he'll never come out. It's a real wtf situation.

Take a shot at their legs. Often that will knock them to the ground and out of the round of retaliation but only if you do enough damage. .50 caliber always does the trick for me although a bit noisy.

Can you use burst fire in JA1? Works for me in JA2 (most of the time).

Well, I think only good solution it's save&load. I'm playing JA 1 now too, with half of sector free now. Enemies seems to interrupt you in same specific moments but when they shot at you or throw granade they not necessary must hit you, it's in little randem so keep loading :-).

Nope. Burst fire is not an option in JA1.

Yeah, that might be the only way. I can't imagine anyone who can complete the game without losing a single merc, without saving lol