1. Is it necessary to install the 1.3 patch? Is it already integrated in the gog installer or should I download it?

2. What is the optimal number of labs recommended for research, i used 3 tops and some research times were fairly long even then, should i use more?

3. Are all the game triggers Laputa lab research related, or some are related to eg. number of my provinces, bases etc?

4. is it worh investing in cyborgs/psionics, I see humans more versatile because of their superior armor more room for training, 3 vs 2 skills?

5. Is it worth producing regular ammo if i research the AP variant?

Great game, too bad i couldn't do my first run on Veteran, damn Reticulans decimated my team in a matter of seconds with their laser fire. Back to easy for me :)

gog version is 1.2, while 1.3 is not necessary, it is recomended. Use as many as you can keep running at the same time, I have a game (endgame though) where I find 10 energy labs to be barely sufficient for my needs. Most are research related, but not all. There are some for other events, but I don't want to spoil it for you. Cyborgs can get items with bonus to strength, agility and dexterity (arms and leg slots), and a few more interesting gadgets. They also have a bit higher hit points if I recall correctly, but the limited inventory space is a killer for me. They can fill front line roles easily though.
Psionics so far make for me the best snipers, especially since the inventory constraints ain't that harsh then. They are also the only ones who can use psionic weapons, not sure if you'll need them or not. While there are differences, I'm not really sure if it's worth carrying 2 types of ammo with you, and I can't recall any specifics for the vanilla game Try grabbing ShadoWarrior's Weapon Rebalance Mod, and for even more fun, combine it with Heroic Assault.

GOG version is 1.21-like (no-cd and Win.7) Use as many as you can (with factories), as long you can afford them (by first improving Knowledge Level in the bases where you need resources to pay tracks). Just a tip: To better control the spread of Cultists, you must allow them one last base (the poorer...). As you want. My rooster is 6 humans, 3 Cyborgs, 3 Psionics.
Il like psionics for their psi view: they make good scouts. I don't think so (but I'm not sure). In hardest game, looted regular ammo are used in missions where better ammo are not needed and are to be saved. I play vanilia on Super-Hero :) The first encounter with Cultists will rape you: Don't worry, this is the thoughest part of the game: Ambush, save and reload often..

Thanks for the great tips, as for modding the game i was thinking about that, but first i want to finish the vanilla game and then i will add some mods.

Will the 1.3 patch break my savegames if i apply them now?

http://www.gog.com/en/forum/ufo_series/ufo_aftershock_1_3_fan_patch_released/post3

High-end psionic equipment is really good, and cyborgs with big machine guns or dual-wielding SMG's are super, super potent.