Yes to using a spare car battery to run the starter box. Might be easier and safer to use some removable terminal clamps wired to a deans plug rather than clipping alligator leads to another set. Be aware that the battery will put out a lot of current and you don't want to have them touch especially with you in between the connections, or sparking near nitro fuel.

The portable jump starter it depends on how it works, but should also be possible.