Depends. I almost always buy clothes and shoes in actual stores, as shopping for them online is a wasteful hassle. There are also some shops that I enjoy visiting, like second-hand stores or Asian supermarkets, where it's interesting to just browse and buy interesting things I wasn't specifically looking for.
On the other hand, I always buy stuff like electronics online. Electronics stores are more expensive and have a way smaller selection, so I don't bother with them. Generally if I'm looking for something specific, buying it online is just more convenient.
Technically yes, but they didn't actually require it in the beginning and they even sold it in regions without PSN.