Moss usually is a problem where a spot is too wet, shady and soil has no nitrogen in it. Grass can't compete with moss as this situation. There are some chemical you can buy in Home depot to kill moss. But better way is improve the drainage of that spot and fertilize it, and seed it with shady mix grass. If grass grows well, weed can’t survive.
It is always helpful to add some soil.
Seeds needs to touch the soil. If you rake the lawn a bit, allow seed to touch the soil then there is no need to dig all dead grass out.
never use fertilizer with weed control, never! never! never!
This is why ontario will ban all pesticides use. Killex is great selective herbicides. It is very safe for human, but people start to abuse it. It is sprayed to whole lawn or mix with fertilizer to use on whole lawn even only few weed is there. Table salt could be a poison when there is too much, how about a chemical. You don't need to use on the place there is no weed. It would kill the weed but not preventing it. Hand spray individual weed only, it only take very small amount.
And fertilizer with weed control would kill young grass too. If you use it with seeding, it is a waste time.
After seeding and laying sod,if no rain, water them.