Can I walk in here to sit and study? Or do you need some kind of access premission? If not, is there an area designated for studying (not cubics or room!)?

Yes you can just walk in

There are several quiet areas which you can study without interruption. It also depends what time of day you come as there are several groups of kids that come in to play on the computers and in the teen rooms; they can be a bit noisy at times.

Feel free to walk on in and study your heart away

You can! No permission is needed.

Yes, you can

Yes you can. Also, membership is free.