Moss killer won't kill grass if applied at the correct amounts ...

Moss grows in lawns that are badly drained and/or not receiving enough light.

Drainage can be improved by spiking and sprinkling sharp sand into the holes. If you have trees blocking a lot of the light you could consider thinning them out or raising the canopy .

You can also buy lawn seed specially formulated for shady areas.

Moss can be killed using a granular weed and feed which includes moss killer but if you don't solve the underlying problem by improving drainage/light levels it will return

Eliminating weeds is very easy. Just water on some Verdone Extra lawn weed killer. Verdone is designed to kill weeds but not grass

Once you’ve got the drainage and light sorted out it is very easy to keep a lawn looking lush.

.1. Don’t cut the lawn too low( an inch is ideal) but cut it every week. If you cut it lower than an inch ( unless you have bowling green type grass species) there’s not enough leaf from the grass to grow properly. If you cut it less often the grass will snag on the mower blades and wreck the look of the grass.

2. Water on Verdone Extra if necessary to kill weeds in Mid April

3.Sprinkle on a Granular feed to make the grass grow quickly in early May

4. Water on Verdone extra in Mid July (only if required to kill any other weeds)

5. Mid September scarify lawn this can be done with a leaf rake or depending on the size of lawn you can buy a cheap electric scarifier or hire one and add an autumn feed….(this has a different formulation to spring feed)

That may sound onerous but on an average sized lawn .( say 30 feet by 20 feet) all but the scarifying shouldn’t take more than 10 minutes per operation..

Once you’ve scarified you can probably get away with doing that 2 yearly.

The above method assumes you’re prepared to use weed killers/fertilisers. If you’re not you’ll need to remove the weeds manually which is a big job.