I am confused on the UAE Visa on Arrival as to how it works.

My understanding is the Visa on Arrival available to the citizens of the eligible countries is free. It is issued at the airport of entry, such as DXB or AUH, upon arrival. Is it correct? Does that mean the immigration officer would stamp the passport or you go to some window to get it done?

What I am not clear on how it works is, if you exit UAE to the neighboring countries, upon return, you would get a new Visa on Arrival, is it correct?

For that matter, does Qatar has similar set up? I am under the impression Qatar's Visa on Arrival is not free and actually rather expensive.

TIA for answering my questions.