Plumbing questions

New house owner here, a couple of weird plumbing things I'm noticing and not sure how big of a concern they are. All of these are very sporadic.

Possibly relevant things to note, I live in the US, we do not have a basement, do have a crawlspace, are connected to the town sewer lines, have lived in the house for about 2 weeks and it was vacant for a month prior to us moving in (with occasional visits and contractors.)

1. A couple of times, but only a couple, the bathroom sinks have made a sound when flushing the toilet. Maybe once this happened with the kitchen sink but I couldn't be sure. Not sure if this is something I should be trouble shooting or I'm overthinking it.

2. We've had occasional sewer gas odors. I've run water down the second bathroom's drains just in case it was due to those being unused, but I can't tell if that fixed it because it's inconsistent. Anything else I can/should do?

3. The main suite shower is a circular rain style shower head. Occasionally, hours or even a day after using it, it'll just run water, the way you'd expect it to drain out of the shower head after turning off the shower. The internet suggested this could be just something where the water is held in the shower head until air/water pressure shifts and it can escape. It's also possible that this needs a vinegar bath to clean up some hard water scaling. Am I on the right track?

4. One of my toilets keeps running/not running when the float gets stuck. I've fixed that before, though the last time I did it, it was a rubber float on a stick and this is some plastic contraption. (I am discovering home repair makes me feel like a 72 year old grumpy old man. ) Pretty sure I can clean it and see if that fixes it, adjust the screw on it, and replace it if needed. But any tips there besides a YouTube video or two?

Never owned a house before so any advice is worthwhile.