How to ask for more details from a US university professor without being rude if he says I should apply through the university?
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.