What is the average royalty a fairly new author should expect to get? And are they negotiable? What about if you've already published a couple of successful books with that publisher, should you try to negotiate a higher royalty for your next project? And if so, how do you go about that?
"Average" varies between publishers. Some base royalties on the cover price, others base it on the wholesale price. New authors can be between 6 & 10%; established authors can go higher.
If you want to negotiate a higher royalty, say to your agent or publisher, "I'd like to negotiate a higher royalty for this book because. . ." and you need to have good arguments for why your book is going to sell like hotcakes. Some will negotiate, some won't.