a robust lawn tends not to have problems with weeds when there are no bald patches unwanted weeds tend to have much less room to incroach on your lawn.
yes thickening your lawn will stop weeds you should aim for a thick 3/4 inch from the base up also lawn sand promotes strong growth and you get less weeds
Hypothetically, yes, in that it will literally limit the amount of water allowed to reach the weeds. However, thickening seed is never really an appropriate substitute for a good weedkiller.