Why is -12v connected to GND in this schematic?
I suspect that this circuit is intended to use a single 12 volt power supply, with the negative terminal of the supply connected to the circuit ground.  The power input labelling is misleading - it appears to imply a total 24 volt supply (+12 and -12) rather than a single 12 volt supply.

Test point 4 and the test point connected to Ground are just handy spots to connect your meter to measure the supply voltage - you can ignore them.

Does the place you found this circuit recommend any particular op-amp?  If not, I expect any op-amp that will work from 12 volts will do.

When you want to ask questions about a circuit you found somewhere, you should include links to the source (and you should look around the source - it might answer your questions...)