'Friends think my colleague is a rebound choice'

I broke up with my boyfriend two weeks ago and am quite attracted to someone I work with. I think he likes me too, because he chats with me often and asks about how I'm doing, but I'm not sure. I want to ask him out. My friends want me to avoid dating him though, because they believe he is just a rebound. Are they right?
I don't know who this person is, but your friends know you and presumably care about you, which is probably why they are warning you from getting into something so soon after the end of your last relationship. Rebounds usually happen quickly after relationships end, probably because people who are grieving need someone to sympathise with them. They often confuse this sympathy with something else and transfer old feelings to new people without stopping to examine them very closely. It's normal. At the same time, you do risk being hurt again, so I suggest you take your friends' advice and give it some time before you plunge into something new. Give yourself time to heal.

I went out on a date with someone two weeks ago, and he has been e-mailing me often since then, asking all kinds of questions. Some of these are very personal so I don't know if I should respond to them. Is that rude?
It's sometimes easier to respond to something online than it is in person while having a conversation face to face. Considering you barely know this person though, you should probably do exactly what you would in real life, which is be circumspect. This person probably doesn't mean any harm, but you should probably find out more about him first before you divulge information to someone who, at the end of the day, is still pretty much a stranger in your life. Also, if you're not comfortable with some questions, you are well within your rights to point that out to him. He needs to understand what your boundaries are too.