Is micromanagement of early units "required" by Protoss?

Are the Protoss fairly micro heavy in the early game?

I agree with other posters that Protoss benefit from micro, but that so do all the races. Protoss do get an early "caster" unit in the Sentry, and do benefit from micro to save wounded units since their shields recharge, but then zerglings benefit from careful surrounds and marines benefit from grouping and stutter-stepping.

It's true that you see pro players using forcefields to incredible effect, but you'll also see them do amazing things with reaper scouting/harass, expand-blocking with workers, and so on. Use these tactics if you can, but they're by no means required unless you're in the top levels. At my level I rarely see sentries, let alone good forcefield usage.

Can an underpowered computer limit your ability to micro in a game?

Sure, but if your PC is lagging enough to mess up your micro in the first battle of 10 vs 10 units, it will be completely unplayable in the later stages of the game. Therefore if the game is still playable in the late phases when you have big armies, you should have no problems early on. Later-game micro could be a problem, when you have tons of units, but that varies PC to PC and you just have to try it out.

Protoss can be micro-heavy, just like the other races.

For less micro-heavy play you can do zealots with speed + stalkers (obviously speed comes in later) but the way I keep stalkers behind is just to have them in a separate group and tell them to follow one of the zealots, then only attack-move with the zealots. Against zerg if I know they're not going air (or banelings I guess), you can even do pretty well with just zealots with speed, which is about as point & click as it gets

Forcefields are great, but they do require micro. I've played many successful games without sentries though, but depending on how far you want to go, you will need to use them eventually.

I think you under estimate the amount of micro for Zerg though

Zerg has that problem (keeping units together in the right order) the worst actually because lings are super fast and unless you're careful they get separated from the rest of the group. Roaches are also faster than hydras, but you want them in front, so the follow trick doesn't work as well with them either.

Lings actually benefit a lot from micro, assuming you have open ground to do it. Splitting into 2 groups and getting a good surround often means the difference between winning and losing an encounter. Especially if you get a good surround that prevents the opponent from effectively kiting (say with stim).

Additionally with lings you sometimes want to use their speed to not encounter the main army, but run past them into the opponent's expo to wreak havoc.

Terran bio has it easy, since M&M move at the same speed and both have stim. You still need to do the stutter-step thing for kiting usually, but that's about all you need to know about microing them at least until you get to diamond level.

Tanks require more micro, and they're somewhat of a staple, then there's doing drops which also requires micro but you don't have to do drops.

1 . Are the Protoss fairly micro heavy in the early game?

Protoss has usually more expensive army that has lesser amount of units. I would say micro is especially important for Protoss.

Let's talk a little about early game when Protoss has 1-2 zealots and 1-2 stalkers. If you compare that to opponents army - that could be around 10-16 zerlings OR 4-6 roaches OR 2-4 marines and 1-2 marauders OR 3-4 marauders.

In any of these cases Protoss army is need to be microed very well. You MUST to pull back you stalkers back when they are low health (they have good speed and can retreat pretty quickly (if not surrounded). If it is too hard - go back to nexus and take your probes to cover stalkers. Try to keep you stalkers survived and in the same time - build few new zealots.

Don't give zerlings to surround you. If you see them running to your back - just get your forces back too. And try to use probes. They are very effective in conjunction with you army (probably the main thing: they will not give zerlings to surround your army and still do pretty good amount of damage).

2 . Can an underpowered computer limit your ability to micro in a game?

I don't think so. In worst case you will slow down game for every player. But that shouldn't prevent you from microing. More over, with slowed down game you will have more time for microing.