You can do all of the things that you suggested, or any combination of
them, but I don't think you're ever going to be happy with the result.
Once you go down the "overcaring for the lawn" road there is no end to
it.

Let me tell you what I do for my lawn, and it looks great. I do
basically nothing. I mow at the second from the highest setting with
my mulching mower, and I let the clippings lie where they fall. I do
not provide any supplemental water. This makes the roots go deep, and
the lawn "learns" to fend for itself. (A weak lawn with shallow roots
that is used to being fed from above might look even worse for a while
until it figured out what to do.)

And that's it. Healthy grass has deep roots and is tall enough to
shade the lower parts of its blades from harsh sun. The clippings that
fall decompose and provide nutrients. Grass doesn't need anything else
to survive, honest.