I feel bad that you didn't get a reply so I am going to do my best to cover some information:
1. Phrasing: fast isn't everything. A few things that will elevate improvisation include knowing when/how to let notes "breathe", building tension by ascending/descending the fretboard, and incorporating core motif's (i.e. short phrases that you return to and modify slightly to build layers within your improv)
2. You question about the C chord is opening up a whole can of music theory worms. Can you play Am pentatonic over a C chord? Absolutely, especially since Am is the natural minor of C. The notes of the C major pentatonic are C-D-E-G-A. The notes of the Am pentatonic are A-C-D-E-G. Same notes, different order.
If I had to do a quick summary I'd say you are at a good spot to start listening to and recreating other's solos. I think a great place to start (especially since you are comfortable with pentatonics) is with Angus Young's AC/DC solos. He shreds without having to shred, meaning it sounds way heavier and faster than it actually is. On top of that, he is masterful at blending minor AND major pentatonics together which is a great 'next step' and adds a lot of depth to what might feel shallow.
Hope some of this helps at least a bit...