Hello welcome,
Strictly not necessary to cool down as the turbo should be water and oil cooled, good practice to do it though, drive off boost for the last couple of miles and just let the car idle for a minute when you stop, let it all cool down,
No idea about the alternator, although I presume it just charges the battery at required intervals as opposed to constantly.
Easiest way to buy stuff for your car will be by the nickname given to the front end, classic bugeye , blobeye hawkeye etc. I presume yours is a hawk ?
Bob's are a matter of preference some have problem with aftermarket ones other do not, I'd wait for someone with same car to give a more definitive answer