I just purchased a new townhome and have 13 wall outlets and 3 light switches on one 15 amp breaker. I wonder if that is within the electrical code?

I have my PC, router, internet phone box, cable modem, portable a/c unit and of course other misc things such as lamps, camera and cell phone charges all connected. It recently passed an inspection but It seems it may be too much for one breaker. The portable a/c unit says it pulls 9.5 amps.

Does anyone have the answer about the code? If it is within code, will everything be okay running at the same time?

The outlets you mention are all considered as general purpose lighting outlets, and there is no maximum amount on a residential circuit. The issue is the air conditioner. Everything else will run fine, but the AC should have it's own circuit.