Being quite new at climbing, I love watching Youtube videos of guys like Chris Sharma eating epic overhangs for breakfast, climbing some sick stuff ! All of these climbs however have quick draws up there already and they lead without anything on their harnesses.

How does that work? Do they make a top rope anchor and on the way down put these up?
If so, How on earth do you top rope down an overhang, placing draws?
And cleaning, do they top rope as well?

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No temptation has overtaken you that is not common to man. God is faithful, and he will not let you be tempted beyond your ability, but with the temptation he will also provide the way of escape, that you may be able to endure it. 1 Corinthians 10:13

They charm magic, singing quickdraw fairies to take them up and use holes make by cliff dwelling gnomes for the bolts

<sorry, rough day>

The hard part is not getting the draws there, the hard part is placing the bolts in the first place, drills and bolts are HEAVY. They use a variety of aid/trad gear, sometimes top down (if they can, sometimes the terrain doesn't allow it) otherwise bottom up, drill all the holes then put in all the draws.

When cleaning overhanging routes they get lowered as you would normally, but they clip themselves to the rope running from the belayer to the chains with a draw. This keeps them close enough to the rock that with a little bit of work they can clean the route. If you do this, remember to unclip from the rope before you unclip the last (lowest) draw otherwise you will drag your belayer across the ground.

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Happy climbing
Nic

now if you think about it, you can figure out how Alex Honnold's solo climbing career started
and when he's not available, they usually call Matt Bush