In this context, there's no real difference. In other contexts, there is. If you see someone do something, it suggests that you saw the whole action from start to finish; if you see someone doing something, it suggests that you saw this action in progress. For example, "I saw Mary eat that box of chocolates" means that you know that she ate all the chocolates. If you say "I saw Mary eating that box of chocolates", you only know that she ate some of them: she might not have finished the entire box.

The difference between them do and doing is that 'doing' has a continuous sense, and therefore suggests a longer time period. You might use that for a process where doing that thing took a longer time. In this sense, because 'going out' isn't usually a long process, they are pretty much the same meaning, and 'go' would probably be used for simplicity. Please note that 'sb' is a dictionary-only abbreviation. Native English speakers don't use it in real language.

These are very similar sentences. "A" would mean it has happened a while ago. You saw this occur this afternoon. "B" is describing ...I saw him moving out... He was not sitting with a book or studying with a book. "B" is also the way a person speaks when reporting something that they observed. The last time I saw my sister and brother, she was washing the floor and he was going out with a book in his hand. I hope this helps.