but I have no idea how to use it

Install davx5, connect to radicale, and allow your calendar/contacts access to it.

I’d like to be able to self host my own calendar and contacts. Is radicale appropriate for this?

Yes.

Is it safe to self host a calendar?

Define “safe”.

Can a self hosted calendar still send and receive invites to other calendars?

Short answer: no. You are describing caldav/cardav integration with email.