We lived in a 100+ yr old house with plaster walls. We always hung the rods from the wood trim on the Windows. We didn't have a problem hanging pictures or heavy mirrors. We usually just used large picture hangers, the kind with the nail already in them that go in at a slant. If you try to drill a screw straight into the wall I don't think you will get a good solid hold because the screw will go completely through the plaster and wood lath used to hold the plaster on it. You may be hitting a nail in the lath which is why the bit broke.. I would, go to the local hardware store and ask them what to use to hang curtain brackets on a plaster wall. They should be able to help, surely there is a fix for it.

Get a really high quality stud finder and say a little prayer. When you hammer nails to hang a picture, put a little piece of scotch tape on the wall where you put the nail.

Hire a pro to hang these for you. It will be money well spent and not that expensive.

Being familiar with my granny's house items were hung from wood frames. You might consider silicone to glue hooks to plaster. I would not attempt anything heavy though. Good luck.

We live in a 80+ year old house with plaster wall.

For curtain rods, we use wood frames. Don't want to take chances. Other than that, we've only used nails that PO left. Never drilled any holes since we moved in 10 years ago. Command hook is great for things like Christmas wreath that hides that plastic hook.

This article might help you -- although I never drilled anything to our wall ourselves.

Good luck!

https://www.thisoldhouse.com/walls/21014946/choosing-the-proper-fastener

A couple of people have mentioned hanging things from "wood frames". Can someone please explain what this means?

wood frames that surround the window (trim)

This is a house built in 1905 we just used the wood frames since those walls were plaster and lath