What kinds of Conservatories are there in the states?

Hello.

In America, is there a universal music education association or something like that? For example, in Canada, the Royal Conservatory gives out grades from Grade 1 to ARCT in music proficiency, and those grades are often necessary in order to get into a music university? There are also grades for theory: Grade 1 and 2 Rudiments, Grade 3 and 4 harmony, and Grade 5 counterpoint. What do they have in America, just out of curiousity? What organization gives out music grades, if there is such a thing?

There is none. There are a patchwork of state and local organizations that give out grades, but their systems vary greatly and there is no national standard. Entry into conservatories is generally based on audition (or portfolio, for composition).

I will note: most American conservatories recognize both the British and Canadian grades; and ABRSM exams are available in most of the US.