Opening up NES console

to my knowledge no, all screws on the NES are phillips screws.

However,

If you see some funny star shaped screws then you need what they call a gamebit. Check ebay. There are two sizes of "gamebit" so if you need the tool check you get the right one.

The connecter can be cleaned and bent upwards. Normally replacement of the connecter is unnecessary.

I've opened up several NES systems and they all had standard philips head screws. No problem getting in.

You have to remove the motherboard to get the new connector on, and its a tight fit, so you'll have to apply some pressure.

The real trick to reassembly is getting the black cartridge holder in place so it works right. No reason for it to be there except that the NES is trying to look like an old fashioned VCR. Clever, except for the fact that the top loading vcrs were history by 1985. Anyway, experiment with how tight you have it screwed in, and eventually the cart loader thing will stay down when you load the game in.

Also, start working with the NES by putting in carts. But not the Mario Brothers/Duck Hunt game. The earliest NES games have a thicker circuitboard that will be hard to remove from the new connector. Try other games and after a few carts the connector will be ready for anything.

Good luck.