Wire Identification
 

Can someone please tell me what the green connector is for? Mine is broken...

Also, in the third photo, what is the cut wire for ? Should I connect it to the ground next to it?

Thanks.

In the third picture, that's supposed to go to your Coolant Level Check Sensor.
It BUZZES VERY LOUDLY (Some of you experience this) until you get the system bled. If I were you, don't ground it or else you might run low on coolant and never know.

The first connection looks to be a Water Thermo sensor. You'll want to replace that.

its not supposed to be grounded at all, the orange wires should be directly connected. As w0ppe said this is so when your coolant is low, the car will buzz. Right now is is grounded so that it wont buzz if it were just cut it would buzz. Its not really a big deal mine is grounded. I know how to check my coolant regularly so im fine.

Thanks for the help!

Get another water thermo sensor (first two pictures) so the ECU knows what your collant temp. is. Also get another Low coolant sensor. Most know how to check coolant level, but that won't help you if you bust a hose and don't see the temp. gauge pegging.