1) What is the best way for installing mods at the moment? I plan to use lots of mods including FCOM.
BAIN (Wrye Bash's built in installation system). You'll need Wrye Bash, and therefore Wrye Python, to do that.
2) What are best performance increasing mods? I remember using Streamline and some texture and model replacers.
Oblivion Stutter Remover, and Streamline. Also, PyFFI. Possibly, cleaning some mods. Oh, and Quiet Feet MAX - unless you have a proper sound card, maybe. You could also try disabling music altogether. Personally, I find that quite immersive, but YMMV, natch.
3) Is HGEC still the most popular and supported body mod?
Definitely. perhaps followed by Robert's Male. Then all the other female body types. If you like HGEC, check out EVE HGEC for an easy, all-in-one body, clothing and armour replacer.
4) I remember a mod called Unnecessary Violence 2 being made at the time when I was last playing. If it's done, what are your opinions on it?
Not done yet. Deadly Reflex 6 (
beta) is out, however. And UV2 can't be too far away...
5) Lastly, I'm looking for archery-oriented mods, so all suggestions are welcome.
I recommend either FCOM Archery (beta, I think) or Duke Patrick's SCA Archery.
Also, make sure you check out http://tesivpositive.animolious.com/, in general, if you haven't already. Even if you have...
edit: Oops, I forgot about levelling mods. Well, the most popular would be nGCD + Progress, Realistic Leveling, and Oblivion XP. Check their threads here for details.