Quoted:
Does the repeater broadcast it's own PL tone back to my HT to open it, or does it do an "open" TX?
Some repeaters allow the PL tone being transmitted on the input frequency to pass straight through, so that it can also be heard by other radios listening on the output frequency. Others use a high-pass audio filter that blocks it.
Typically, when using a repeater, you only enable the PL tones for your transmitter - not the PL squelch for your receiver. So, even though a PL tone is required to transmit through the repeater, nobody on the receiving end needs any PL tones to receive it.
Note that there are exceptions - Sometimes, several repeaters on the same output frequency share the same coverage area. As long as the PL tones they pass through are different from each other, it will be possible for users of one repeater to "ignore" signals from the other repeater, simply by setting their PL squelches to the PL frequency of their desired repeater.