Can an old-cement garage floor be painted in sections?
The most important step is cleaning the best 2 part epoxy paint can’t stick to a oily floor.
First it needs to be cleaned 100% I suggest an acid wash using muriatic acid and water, 3% to 10% for badly oil stained floors, the muriatic etches the concrete as it dose it is neutralized with the weaker solution, then a good rinse 2 or 3 times let dry and you are ready for paint.
The quality of the paint is the next most important thing. I use 2 part epoxy paint made specifically for garage floors rustolium has a good product out there I have used several times
Don’t go cheap or use 1 part epoxy paints, a friend followed my cleaning advice
But went with a 1 part epoxy that when car tires sat on it started peeling the paint up (hot tires can cause failure) I rented a shot blaster to clean this off it took 2 full days because he wanted to do it right the 2nd time.
Follow instructions I use a heavy nap roller work from the back wall to the opening.
I would recommend using the color chips or an abrasive powder as you roll the paint scattered on the surface it doesn’t take much but you will thank me if you ever spill antifreeze on your floor (it is slicker than ice with no abrasive) I recleaned my shop and added a thin 2nd coat with abrasive sprinkled it still looked awesome but I poured some antifreeze and water on the new surface and could walk on it, without the abrasive I could not stand.
Once the floor is cured 24-72 hours depending on brand it is ready for abuse and is really easy to clean oil up kitty litter to pick up the bulk then a few squirts of laundry soap or dish soap and the floor looks like new again, I use a 3’ squeegee to push water out.
Depending on how rough or The porosity Of the surface you may need more paint than the can says it will cover, I think the ones that said 300sf / can were glass smooth floors rougher plan for 250 sf if it says 300.
Those are the things I have done many times for myself and others.  hope it helps.