TP1 is a "test point." The resistors form a voltage divider, so you can safely measure the voltage across the coil. Don't connnect a scope probe directly to the coil. You run the risk of damaging your scope.

You could make a physically smaller coil. It just means the field will be concentrated in one spot, intead of spread out over a wider area.

The Q of the transmitter coil is just the inductive reactance of the coil divided by the DC resistance of the wire. The Q of the receiver will be determined by the inductive reactance of the coil divided by the load impedance. Shoot for a Q of 40 for the transmitter and 5 for the receiver.