If you remove everything driven by the bad transistor, that will be safe, yes. Sometimes there are multiple flashers/coils hooked up though. In this case The 'Flashlamp Type' column on the coil chart shows two #89s on the playfield and one #906 on the backglass. You could also just take the whole 8-driver board out and play the game without it safely while you work on it.

Q16 looks correct, yes. When testing transistors, I just compare the diode readings with other transistors on the board. It's all the same circuit repeated, so they should have similar (within ~0.1V) readings. If it's stuck on you're almost certainly going to see a reading near 0V somewhere

Yes probably the drive transistor. Select diode test on the meter and take two measurements. Center leg to out side leg and center leg to other outside leg. Depending on what type of transistor NPN or PNP depends on whether the red or black lead is on the center leg. Try one way then the other. You should get between 0.4V to 0.7V (ideally 0.6V) readings if it's ok. With the leads swapped around you should get an open reading. If the transistor is shorted one reading will be about 0V.

Remove the flasher. They get very hot and will melt inserts, etc. the advice above is sound for testing the transistor; it’s likely shorted to ground.