Partial answer:
Rover technology has evolved a lot since the 1960's and 70's!

From this answer:
The Lunokhods were controlled in real-time from Earth (long article well worth reading), exactly as you say. A camera relayed images to Earth (one image every 7-20 seconds) and a five-man team (driver, commander, navigator, radio antenna operator, and the flight engineer) would control the rover.
Lunokhod were driven life by beings on Earth, and Apollo LRV's were driven by beings on the Moon.
All of the robotic Mars and Lunar rovers and landers since then have had computers with memory, and received instruction sets that they executed afterwards.
That doesn't mean that there have never been situations where instructions have been sent and results received followed by more instructions in near-real time! But the idea has always been to avoid that.
(I think there's a possible new question there)
Certainly there will be engineers (as well as us as home) sitting on the edges of their seats watching things happen in the early hours and days after landing, but to minimize risk these activities are all either pre-programmed, or downloaded in bulk after landing.
I think there is an answer somewhere on the site about new software being downloaded to a Mars rover once it lands, but I can't find it yet.
Instead, here are some related posts:

All Mars and lunar rovers ranked by how far they've driven. Credit: Bob Al-Greene / Mashable
Sources of data: NASA, JPL-Caltech, GSFC, Arizona State University, China National Space Administration
From How (the heck) did Lunokhod 2 drive, navigate and survive a ~40 kilometer drive over four months on the Moon using 1970's technology?