1. Yes. As a -part- of RTC (RTC by itself may be a rather complex piece of software)

2. Now that's tricky :) The reason is that in great most of '52 derivatives either of timer 1 or 2 must generate baud rate for serial to work... so your procedure would be: Timer 2 runs as usually. Timer 1 by some external signal (pushbutton?) stops counting normally and starts generating baudrate. New value is sent over serial line and recorded somewhere in memory, serial connection is shut down and timer1 is reset and started with the newly downloaded value.

3. Yes, but if you stop the baudrate generator while serial transmission is underway, the transmission will be broken, any data transfer underway will get corrupted. But I think time taken to reset Timer 2 may mess up all your measurements.

BTW, you never mentioned timer 0. Don't you confuse Timer 1,2 with Timer 0,1 ? Timer 2 is quite a bit different from the other two.