1. 4GA
2. removing, easy, replacing, not so easy... you will need a crimping set, and its a pretty big lug... best bet is to find the right size lug, and ask someone at jaycar to put it on some 4GA for you... no point buying a crimping set if you only use it once
3. yes, or even the terminal if its just as close... if your going to make your own, make sure to get a good solid connection, and sand any paint back...
4. 4GA the bigger the better theoretically...
5. If the battery is sealed i wouldn't worry about it, it seems like a previous battery has corroded... keep an eye out for a replacement though... or get that one sand blasted and painted if its not too bad...
the cable joiner is a temporary thing... it also seems to be bare metal, which is bad for a positive wire in a negative car... get the right size ring on some long 4GA and replace the standard one...