I have spent too many unhealthy hours reading blogs and websites filled with advice on queries for far too long. From what I have learned, everyone wants something different but they wont all tell you what it is that they want. So I have a few general questions. 1) If you have a website for your book or work is it appropriate to give them the address in the query?
Put it in, but there's almost no chance we'll look at it. Still, it doesn't hurt.
2) On some sites I read queries where it looks like the first half of the query is sucking up to the agent and has nothing about the book. If I am querying an agent they should know what I am after. Their approval. Is it necessary for me to try to tell them why I want to work with them and list all of the books they have published that I have read?
Throwing in a reference to a book the agent represents isn't considered bad. It shows you did research on the agent and are not just mass-querying. In some agencies it gives you points. Honestly, I see it so much I just ignore it and focus on the book that's being pitched, but again, it doesn't hurt your query, so you should do it.
3) Early on I was over excited and sent out a query to an agency I quite desperately wanted to work with. They rejected me because they didn't feel a connection, but said it was a great concept. This prompted me to reevaluate the query and the book which turned out for the best. Is it ever appropriate for me to resubmit to them? If so, how long must I wait?
A couple months, but don't expect anything. It will probably be rejected again. There was a reason the first time and it may have been unrelated to the format of the query letter. Like "Ugh, I've seen too much of this lately" or "I'm not taking on new clients now unless it's specific genre."
4) I have no credentials that relate to my writing. I don't feel I should have to tell them anything about my self if my writing conveys that I am the best person to write this story. It takes up more of their time and they don't care who I am, I don't mind that. I'm arrogant but not egotistical. However most agents websites say "tell us about your self" in their criteria. Do I have to if they request it?
When they say "tell us about yourself" it means "tell us what writing credentials you have, and if you've written non-fiction, what credentials you have to write this specific book." You don't need to put in any other biographical information. By the way, I can't stress that last part enough. If you have written non-fiction (other than memoir), you should have some credentials proving why you're qualified to write a book about your subject. You know, degrees you might have, research you might have done. That sort of thing. We don't see enough of that in non-fiction proposals.