How to ask for more details from a US university professor without being rude if he says I should apply through the university? I'm a BSc holder looking for grad. studies. I contacted a professor from a good US university (not Ivy League) about his work and publications which I liked very much. I told him about my research background etc, his answer included the following points:

1- Telling me that I have "a very good background".

2- That I must first be admitted to the university and he can't directly take students.

3- The fact that 1st year is not so research-oriented and he can't say if he will be able to take a new student.

4- Telling me that I should apply.

This I think, isn't a specific case just for me so I'm going to ask here.

Funding is very important for me, I cannot fund my study even for a semester. Where should I go from here and what to ask to make sure of funding my Ph.D. study from the begining? Can I make sure I'll have a RA position before even applying?
In the physical and natural sciences in the U.S., it is almost always the case that Ph.D. students are funded, meaning not just having tuition paid for, but also having a stipend / salary sufficient to live on. I'm sure there are exceptions to this, but I haven't heard of any, and I will guess that they are rare. Also, importantly, this stipend is tied to work of some sort, typically either teaching assistantships or grant-supported research positions, with the general idea being to transition from the former to the latter in a year or two. There are various details -- e.g. making adequate progress to degree, actually finding a research advisor who will take you and who is likely to have grant funding, etc. -- but in brief, when applying you should not be worried about the things you're worried about. 

To directly answer your question, though: don't pester the professor you wrote to with funding questions. (His response is very similar to the one I usually send!) Check departmental web pages or administrative / admissions contacts if you have specific questions about this. Though it does matter whether your potential advisor has a track record of funding, and how likely he/she is to take on students, you won't get a clear answer about this, especially because it is quite difficult to predict what will be the case ~2 years in the future.