Can you walk from gate c to gate a?

All PHL terminals are interconnected after the security. You can walk from C to A. I did it from A to C yesterday. There is also a shuttle bus within the security area from A to E and E to A since it is quite a hike.

Yes you can

After TSA you can walk, sometimes that's quicker than waiting for the bus. Before TSA, there is some part where you need to walk outside the terminal building.

I'm quite sure you can. It's D you must shuttle