Okay, my hunter lv10 now. Which skill/talent is good for soloing and pvp?

Totally up to you, but I reccomend getting at least 20 (I think) points in Marksmanship for Aimed Shot and Hawk Eye (+6 yards I think), but that's my opinion.

Then Survival/BM. Just test out with the talent calculators on the homepages.

Another question, when do I feed my pet ( owl ) ? I don't see any indicator that suggest it is hungry or full. I just feed it when it is content.

The indicator is the emoticon beside its name and also in the pet stat panel. When its content you can feed it more to make it happy. If you don't feed it it will become unhappy and eventually leave you. The happier your pet is, the more damage it does.

When the little emoticon goes to content just feed it and keep it happy. That's all I do anyway...

Can a hunter take herbalism and alchemy? I see websites suggest hunter to take skinning/leatherworking or mining/blacksmithing/engineering. I'm interested in alchemy because I want to create red potions ( hp potions ) for myself.

You can learn whatever profession you'd like, there are no restrictions. But you can only have two major professions (Skinning, Mining, Herbalism, Alchemy, Enchanting, Leatherworking, and Blacksmithing). You can unlearn those skills, but you will lose all points and recipes if you decide to relearn it.

Heh! because of the 2 minutes cool down effect after drinking a red potion. It means I can't drink all those red potion that I've created like water. Might as well take another profession.

Herbalism and Alchemy is good, but I took Skinning/Leatherworking at first, then realised my mistake at about 40. I changed to mining/engineering as Thorium Bullets (which can be changed into Thorium Arrows) costs 1g 60s per stack, and I have a 16 slot quiver, so that's a lot.

Just go with whatever you feel like. Skinning/Leather will stop you buying armour as most of it is +agil, what you need. Engineering can be fun with all the trinkets and items. Alchemy is useful, as you said, for health potions, but also has other buffs that can be used.

I constantly find myself needing potions, so I've created an alt and trying to powerlevel him so I can get some good health potions.

Alchemy and Herbalism will get you a TON of money, whereas Leatherworking probably won't, also, you'l outgrow leatherworking stuff around lvl 40, when you can use mail. The mail created from Leatherworking isn't that good.