Should I apply for a position that I am interested but not competitive enough? I am interested to an assistant professor (AP) position. The topic is very suitable for me but I think I am not competitive enough (not enough paper etc). Also, I am willing to take a lower grade position (In my country there is research assistant professor (RAP) position, which is between AP and postdoc). However, the job abs did not state specific requirement for papers and grants (like X papers or Y grants), so technically speaking, I am qualified to apply. My questions are:

1) Should I apply and see if I can get an interview, to get in touch with them?

2) How do I express I am willing to take a lower grade position (such as RAP)? 

3) Is there any better way to express such purpose, which may be better than applying for the AP position?

4) If say a few months later my papers are published, and I think I am more competitive, can I apply again for the same job (assuming it is not filled)?

Any comments and suggestions are appreciated, thanks!
Let the hiring committee decide whether you are competitive, rather than assuming you are not. Apply and make your best case that you are the best person for this job. The decision will be made on a variety of factors, not just a count of papers. A person needs to be "fit" for the position and that will mean different things to different people. 

And as for 2), don't do that at all. 

Part of your application will show works in progress, of course. Especially if you have submitted papers that are not yet published. If the job includes teaching, show that you are good at that. Don't leave anything out. Don't assume that anything is unimportant.