They do, it is common practice to safely dehorn Rhino in game parks (alternatively some parks will keep all the Rhino in a smaller more easily protected area). However, horns grow and poachers will cut off the part that cannot be safely removed and still get a good yield. I'm assuming that poachers would use tranquilizers if they could because they are less noisy and would therefore be less likely to be caught. However, they are often not very well funded and simply opportunists. Some are though.

And how will a hornless rhino protect itself against predators?

Healthy adult rhinos have no predators (except humans). They are massive. They use their horns to defend their young and their territories.

You'd think so, but here's a video of for example a hippo vs a rhino without (much of) a horn: https://www.youtube.com/watch?v=XW-GX7o7hBc

Also when a pride of lions get hungry enough they'll go after anything, at which point having a horn makes all the difference.