forests are most useful on tundra as they give you more sheilds than tundra. Also, you get a sheild bonus for cutting down a forest (10 sheilds i think) although you can only get that bonus once per tile.
Just a suggestion, a lot of your questions are easily answered in the manual and/or civilopedia. Also, it seems like you just started playing the game. I'd suggest you play a little more and then post any questions you may have in one thread titled newbie questions or something like that.