I have few questions regarding fatigue consumption in turn-based combat.

First, according to the manual, whenever I perform an action that costs more AP than the amount of AP I have left, the same amount of 'extra' AP used will be deducted from my fatigue, eg. if I perform an attack that cost 5 AP while having only 1 AP left, 4 point of fatigue will also be used.

But this doesn't seem to be the case, and the amount of fatigue consumed while performing such action seems to be 2 point regardless of how many extra AP I used.

Second, again, according to the manual, if you run while in combat you will use up fatigue, while walking doesn't cost any fatigue but cost extra AP instead.

Again, this also doesn't seem to be the case. Running doesn't seem to use any fatigue (at least in turn-based combat), so there's really no point in walking. Although NPCs still walk if their fatigue is low, for some reason.

Was I mistaken, or are these bugs, or features?

I'm running GOG release version 1.0.7.4 with UAP 2.0.1

For some reason? It's because they're exhausted, you insensitive clod!

Kidding, of course. The implementation of AP does appear to be a bit wonky. The only time you'll really see it work like it's described in the manual is when you're "attacking" an inanimate object, such as hacking open a treasure chest. When you're low level (with low fatigue recovery, and not that many FT points in the first place) smashing open the thieves' barrel by the Shrouded Hills bridge can be exhausting, requiring you to recover in real time before continuing.

And yeah, just run everywhere; there's no downside. In fact, I prefer to play the game in Fast Turn Based, which skips the walking and running animations during battle entirely, having everyone just pop over to where they would've wound up.

This game was never optimized for real time, anyway; it was added by the devs at Troika's insistence, because real time games were all the rage at the time. So if it feels like a half-baked added-on kludge, that's because it was.