Arduino Mega2560 as ISP to program another Arduino Mega2560

all version, v1 and v2 also, burn the bootloader to the right memory space, the mismatch verification is not a problem of the ArduinoISP sketch but an AvrDude bug. Infact the bootloader work also when you receive the verification error.

You do not need the capacitor on reset, it is tip for other kind of error, if your burning process finish with successfull you do not need of capacitor.
I repeat my tips for you second question, is it possible using Upload via Programmer on a Mega, but you need change your fuses for starting the program. Simply the sketch will correctly burn, but it do not run.