How large/deep are the front pockets?

Deep enough to place your necessary pocket items withour worrying about having them fall out or being uncomfortable while wearing a "tight/snug" fitting jean

I'm normally buy jeans in a 31x32..will the 31 be true to size? or should I go down one size b/c they're pretty stretchy?

Yes depends on how you like the fit. I normally wear a 34 but the ones I got the fit felt slightly baggy and the waist stretched very far. So I tried a 32 and they are definitely a skinny hip sort of look but still comfortable. So if you want relaxed slightly loose fit go with 31 but if you want more of a skinny hip look go for size down. They'll still fit and be comfy.

i want to purchase these. but im a big worried the 33 in lenght since im 5'8 and most of my pants are 30-32 in lenght and 32 kinda makes them baggy.

Im 5'10 and the 33 are too long the 32 fit perfect. I orderd one of each in diffrent colors. I would go with your natural size. They fit pretty right on.