We know that he discovered his dyslexia but was that really enough to turn his grades around? Should we just assume that he worked hard and matured as he got older from the first episode until the last episode of him graduating?

Supposedly, in college in general, there's usually more than one way to get in. Some schools make it so your GPA can be determined from the last 2 years.

I also heard that average students get into a lot of good colleges. If they have the money to attend, and possibly give a donation they can get accepted. Someone has to help pay the aid of the really smart poor students.

In the beginning, Theo was perceived as a kid who did badly in school. Cliff and Clair thought that he wasn't trying or slacking off. When it was discovered that he had dyslexia, they changed their tunes and they apologized for always getting on his case. I would say that Theo worked as hard as he could over the years and it paid off in a big way. From getting D's in the pilot episode all the way to a college graduate by the finale, that was a MAJOR improvement.

Theo's grades were terrible. I suspect Theo "Aunt Becky"ed his way in, with Cliff and Clair paying off some NYU recruiter. ;)