A. When a timer overflows and the ISR code is called, the timer waits for the code in the ISR routine to finish before resuming its count. So a large ISR code could throw off the timer.
No, the timer keep running.

B. When a timer overflows it sets the overflow flag and keeps going, thus the timer is always accurate, BUT you had better hope that your ISR code finishes and gets that overflow flag reset before the timer overflows again.
that is a "bad hope" To have this problem you will need to have a bloated ISR somewhere else.

ad a) and b) the only way to keep reasonably precise time is auto-reload.

D. It depends on what kind of timer you are talking about (i.e. 8 bit auto-reload, 16 bit etc.)
Not really, but T2 has features that T0 and T1 do not.

Erik