Yeah, blue sparks on the monitor port are pretty normal if you try connecting or disconnecting the cable while the Amiga is on. You can probably get away with it much of the time, but if you zap your video chips... that's bad, mmkay?
For the mouse, connect it to the port that says "MOUSE" not "GAME"... I think it's the one closer to the front of the computer.
It seems to have everything. You might want to look under the drive cables to make sure it has a CPU board. I'd be surprised if it were missing if this was sold as a complete system. Other than that it appears to have everything a basic A4000 should have... which doesn't mean it all works, just that it's physically present.