Well, I certainly don't know everything or even all that much in the grand scheme of things, but I am pretty good with grammar.
To answer your first question, using periods is often a matter of preference and either is correct. More and more, people are not using periods though. The main thing is to be consistent with your choice, so don't write an article that uses U.S. once and US another time.
The title capitalization can be a little tricky, but the main thing is to capitalize the first and last word. Otherwise, you can capitalize most words. Conjunctions(and, or,) prepositions(after, among,) and "to" should NOT be capitalized.
Also, it is "Grammar" not "Grammer" ;)