The tip of the tail looks like it is about to come off. That shouldn't be a problem as long as it heals over cleanly- it's a common issue unfortunately.
It's hard to say exactly what the bump is. Does it feel hard or soft? If you touch it does it appear to be sensitive? It's possibly a deformity in the tail bone.
Which coil UVB light are you using? How far is it from the basking site? They all have different outputs and appropriate ranges so it's important to get the right one to fit your setup or else lack of UVB could cause nutrition and health issues. I can help you get lighting fine tuned if you'd like.
It's probably fine, lots of beardies have slight bumps and even warped tails for one reason or another. It's almost no chance of being a tumor. Just keep an eye that the end doesn't continue to shrivel upwards, if you see that then you may need to have a bit of it removed and that's not a big deal really. He should be fine.
It depends, they usually stay but don't cause any real problem. If it's a slight calcium deficiency then just be sure he's getting enough calcium and proper lighting. There's a very slight chance that it could be related to the end tail rot.....I doubt that it is but that may be the case if the infection was spreading up under the skin. But again, I doubt it's that, just a slight harmless bump. If he's getting proper calcium + uvb he should be O.K