Generator Synchronizing

You have multiple questions - I will try to answer them individually.

If any of the voltage / frequency / phase angle parameters are outside of acceptable differences (usually some % voltage, 0.1 Hz or so, and +/- 5 to 10 degrees), and you close the generator breaker, you risk doing severe damage to the generator. Depending on the "strength" of the bus to which you are syncing, the generator will in a very short time be forced to change its speed / pole position. This has been known to (catastrophically!) throw the rotor right out of a machine.

If the phase sequence does not match, someone has wired something wrong, and you will never synchronize because your phase rotation is backwards.

A synchronizing panel usually has the sync scope, voltmeter(s), frequency meter, and two lights (not three). One light will be connected to the generator voltage source and the other to the bus source, and two lights are connected in series. When the generator and the bus are of opposite phase (180 degrees off), the voltages of the two sources add and both lights are on maximum brightness; when the gen and bus are in sync, the voltages are same phase, and cancel (lights off).

When manually synchronizing, you want to get generator voltage same (very close) to bus voltage, frequency same, and control the speed of the gen so that the needle on the sync scope is turning very slowly. When the needle just almost reaches top dead center, and both lights are out, is the time to close the breaker. A sync check relay properly set, with a contact wired in the close circuit, will block operation of your manual close switch if you are too far out of voltage/phase.

You can leave the sync scope in the circuit, but it tells you very little after synchronization because the bus will keep the generator in sync except for an anomaly in generator operation or system conditions. The sync scope would stay pinned at the top, the lights would be off, and the voltage and freq meters would show the bus conditions. Therefore it is usually turned off after sync.