1. Is it possible to change that capacitor to a battery? For a more long term solution. Dont know how many weeks/months with no power before the cap charge is out.
Sure - the ram doesn't care where the juice comes from. If I couldn't leave the system plugged in and play it at least once every few weeks, I'd probably kill myself.... or switch the ram to fram and eliminate the power requirement altogether.
2. Can I change a battery on a cartridge on the fly, meaning that I can put 3V DC into the cart from a external power supply while I change the battery?
Maybe, but I wouldn't risk it. The sole huey containing a battery is the Tennokoe Bank, and it either is already empty from a dead battery or it's preventive maintenance, in which case it's cheap enough that I can buy a second one to backup the backups before swapping batteries.