The only thing you should ever flush is a toilet. That being said, a drain and fill will suffice.

That seems a bit high to me even if it was a top tier interstate battery. I recently purchased an mtx-78 740 CCA for just north of $200. Might want to shop around.

That’s your purge valve, part of your evap system. It opens and closes as needed to introduce fumes from your fuel tank to aid in your air/fuel mixture in the intake. Should be able to find a new connector and splice the wires or if you can get the old pin out of the connector, you can repair it.

Hammer on a 12 point 3/4" or 19mm socket to remove those.