The goal is to get the grass to generate roots and then this will turn into a nice lush carpet. The thicker the carpet the more competition for resources.
I mow at 6" to keep germinating weeds from getting easy sunlight.
Oh that sucks. Luckily here the city even has flyers on how to have more natural lawns, which works naturally against grubs etc.
We have lots of dandelions, especially close to the street. So do the neighbors though they are the religious once a week mowers.
The trick I find is to let them be beautiful while it's mostly a sea of yellow and then mow as it turns into just ugly stalks with blown away seeds. And have a hedgerow so that you only need to mow the part between that and the street.
I've also sown in clover on purpose. Something many will try to eradicate. Stays green much longer and better in summers when the grass just turns brownish. Some neighbors around us irrigate. I refuse to do that. Very sandy soil to begin with (there's sand pits around) and grass on top of the septic system just doesn't thrive in hot dry summers. So we either get clover green, white and red or brown. Their choice.
Dandelions are pretty and seem to survive far better in my lawn than grass does. So dandelions it is. Can't imagine having neighbours that would complain.
I haven’t dropped anything on my yard except for grass seed in 15 years and it’s fine. So what if there are some weeds on it.