If you're pleased with your existing lawn and can match the seed, plus you only have small bare spots, scratching those up and seeding into them would be cheap, easy, and very successful. That's as long as you can match the cultivar you have in the rest of the lawn. Patchmaster is kind of expensive and doesn't do anything you can't do yourself. A bit of mulch (shredded paper being fine...a very light coat...or straw or Penn Mulch or just cover with a bit of dirt and dead grass), a touch of starter fertilizer, and some seed. The rest of the lawn you can slit seed, no problems. I don't have any experience on the subject, but people here say that germination and sprout are very low in an overseeding because your existing grass outcompetes. Still, it should help take care of any tiny thin areas.

Yellow - buy another can of paint and roll the whole floor. Red - use the Sherwin Williams.

The metal parts look like they were “antiqued” with white or light gray paint. If the shelves are wood, can they be stripped and stained a lighter color? no way to tell what you might end up with but you could try having the metal part sandblasted to take it down to bare metal. Might not be cost effective.

Poor son. Someone "updated" the fireplace already and did a horrid job. The floors are beautiful. I would not want to ruin the banister like they did the fireplace, with white paint, but the room does need lightening. The walls are already white and any color will only darken the room. Maybe he will need to invest in a lot of light fixtures. Is the ceiling white?