Especially cell phones, purses and computers?
Perhaps sometimes on very low-budget productions. But normally, I imagine they use props (which they then make their own).
To quote George Carlin: “Well, what other kinds of belongings are there, besides personal—public belongings?”
Aside from low budgetary concerns improv can bring personal belongings in frame. And this if it’s true.
Absolutely not.
Their underpants are probably provided by the studio.
Sometimes they do. Sometimes they don’t.