Sexual harassment; I'm new at this job and my client is sexually harassing me and has threatened to fire me. Any advice?

You can complain if your from an agency and asked to be removed. If not, sorry u have to quit. It takes an experienced person to handle this kind od man. In a rehab my Mom was in, there was a leach who touched women. Two aides had to be in his room at the same time.

Boundries but doesn't mean he will abide by them. If he scares you, no job is worth it.

In the era of #MeToo I was wondering about the police, if there's no agency and the harassment is bad enough. But of course it depends on a lot of things that we don't know about.

Agency? Quit & report.  No agency: Quit.

New to caregiving as a vocation, or just new in this particular job?

Not that it matters all that much - leave.

Then there's the question of reporting the harassment: how did you get the job?