Force carrying particles in general don't have mass. Except that some of them seem to do, which was rather puzzling for some time, but was solved using the Higgs mechanism.
I can't think of an obvious reason the Higgs mechanism wouldn't work for gravitons, but I could be mistaken, it's not exactly the most intuitive area of physics.
Also, keep in mind that the strong force transmits the force between colour charges while also having a colour charge itself, so it isn't entirely inconceivable for the force transmitting the attraction between masses to have a mass.
No clue if a massive graviton would allow for black holes, but it's not entirely sure what black holes even are (especially quantum mechanically). At the very least it's presumably possible for some particles to escape it (e.g. as Hawking radiation).
I can't think of an obvious reason the Higgs mechanism wouldn't work for gravitons, but I could be mistaken, it's not exactly the most intuitive area of physics.
Also, keep in mind that the strong force transmits the force between colour charges while also having a colour charge itself, so it isn't entirely inconceivable for the force transmitting the attraction between masses to have a mass.
No clue if a massive graviton would allow for black holes, but it's not entirely sure what black holes even are (especially quantum mechanically). At the very least it's presumably possible for some particles to escape it (e.g. as Hawking radiation).