1. Are the internal oscillators precise enough to do serial communication?
Yep. Newer parts with 1% internal oscillators are.

As long as the PIC will operate in a moderate environment like indoors. If you plan to use
it outdoors in extreme heat or cold, go with an external crystal. The internal osc will drift
when exposed to extreme temperatures.

2. Do all chips have OSCCON? I search the 16F676 PDF... nothing
No not all of them have an OSCCON register. Most of them with an internal oscillator that
offers various speeds do. So you can select or change internal osc speeds.

The 16F676 doesn't have an OSCCON register. Its internal osc is fixed at 4MHz. It does
however have a factory calibration value tucked away in the last program memory space.
You tell PBP to fetch & load this into the OSCCAL register with the DEFINE OSCCAL_1K 1
option.