I'm sure Gaster has told him not to talk to strangers, given how possessive he is over what Sans learns.

Sans has really only carried a conversation with Papyrus and Gaster. It makes sense that he would suck at it, and just stop talking in the middle of a conversation XD

Sans has a bad habit of crawling on surfaces. He may not understand that you can't do that in public. I would say that he also doesn't understand personal space, but I think he would definitely be taught to stay away from strangers. Sans is just really interested in what she was writing, doesn't understand that he can't take things that don't belong to him, and Siqua is one of the only strangers he is familiar with (and therefore may not feel the need to stay away from her).

Aw cute, you thought I forgot about Siqua's child psychology study? No, it's just not relevant in chapter 2.