Via to Pad Clearance
This is another, yes it can be done, but think about it carefully thing. Usually if you put a via in or close to a pad, it is going to an internal plane. Not having a trace between the via and pad  will provide the lowest impedance path to the plane. It also helps to put several small vias in parallel. There's a problem with doing this though. Having a hole in the pad is going to wick solder off the pad, into the plated via. The smaller the vias the better, but you need to evaluate whether that is a problem in your application.

From the image you posted, I don't think I would put a via that close to that pad. It's going to a trace on another layer. There's no reason to try to minimize the via impedance there. If space is the constraint, try making the via smaller, and the pad if you can afford it.