1. Problem is, not everyone will know that they're supposed to hit Enter to submit, so you're already needlessly frustrating a percentage of your users (albeit, probably a small percentage) by hiding the submit button. Here's a bit more discussion on the topic, from a question I asked on UX StackExchange a while back: http://ux.stackexchange.com/questions/8876/usability-of-hidi...
Indeed. I've watched many friends fill in online forms, and I can't remember a single time any of them have ever used the Tab or Enter keys. They've all clicked on every field and finally on the Submit button.
