I was under the impression it is a good practice to periodically exercise all the stop valves - house shut off ball valves, water heater cold inlet valves, washing machines valves, all exterior hose bibs and interior angle valves for sink, toilets, icemakers, dishwashers etc...

I recently spoke to a plumber and he said that exercising these valves may cause the valves to leak sooner. If you leave it alone it won't leak, if you keep messing with it it may.

My understanding is if you don't exercise it then one day you have to shut water off and it may seize and you are in big trouble?

For my rentals I do two maintenance visits per quarter, to do stuff like test smoke alarms, check WH T&P valves, check AC condensate pumps, change out central AC filters, fridge water filters if necessary, and every 3 months I exercise all the stop valves. Is this exercising of valves good or bad practices?

If this is something that needs to be done, is there a right or wrong way to do it? I just open and close the valves like 3-5 times for both quarter turn valves, gate valves and multi-turn valves. For multi-turn valves I always turn until it's opened all the way, then turn back just a little bit. Is that correct?

sum, i can say that i have never exercised any valves nor have i advised anyone to do it. doesn't mean i'm right or wrong just never did it.
as for backing off a stem from fully closed, i have done that on the advise of an old timer years and years ago.

Packy the reason I exercise the valves is because I saw many conversations on here that goes like this...

"I tried to turn off my valve to repair this or that and the water keeps dripping, the valve doesn't seem to close all the way help!"

"when was the last time you opened or closed the valve?"

"may be ten years ago..."

"you valve has seized and it's not uncommon for valves that hasn't been opened or closed for a while".

I concluded then to avoid this, the valves need to be opened and closed more often, not just when you have to make an emergency repair once every ten years. So I started to exercise them a few times a year, especially main shut off, water heater cold inlet valves etc...

may be it's not necessary I don't know.