1. Really depends on the matchup.
2. You can't chain grab anyone. That's just straight up not true. You can chain grab some characters, though. You should read the thread about chain grabbing to learn all the percents/characters you can do it to. As for combos out of a throw, here's a general rule of thumb. You can dthrow aerial a lot of floaties. And against fast-fallers, you can dthrow/uthrow to tech chase or dthrow/uthrow to jab and then fair a mis tech. I like to condition my opponents into thinking I'm just going to throw into tech chase so they'll react instinctively with a tech. And then I'll throw a jab, they'll miss the tech and I'll fair to punish.
3. Be careful with side-b, and down-b for that matter. If I know my opponent is just going to land in front of me with a move, I'll side-b. Or I'll use it as a combo extender/tech chase. But never challenge someone outright in the neutral with it. Down-b is a little different. Against some characters/players I will straight up raw down-b and it actually works. Just don't get into the habit of doing it too often because then you get ****ed. Like what I was talking about with tech chasing, I'll condition my opponent to do certain things in the neutral and then down-b once in a blue moon when they least expect it. Afterall, my tag is purple killer, gotta make use of that purp :D