Sharpshooter (PHB p.170) has a host of effects on your ranged weapon attacks:
Attacking at long range doesn't impose disadvantage on your ranged weapon attack rolls.
Your ranged weapon attacks ignore half cover and three-quarters cover.
Before you make an attack with a ranged weapon that you are proficient with […]
Tavern Brawler (PHB p.170):
You are proficient with improvised weapons.
Can the Sharpshooter feat be applied to improvised thrown weapons (rocks, chairs, kleptomaniac kender, my d20), and if so do you still need the Tavern Brawler feat to make it work?
So far we know improvised ranged weapon has range 20 feet and 60 feet with disadvantage.
Bullet points 1 and 2, Yes
When attacking with an improvised weapon you are still making a ranged weapon attack, so the first two bullet points apply.
Bullet point 3, no
Point 3 requires "Before you make an attack with a ranged weapon that you are proficient with…" and improvised weapons are not actually "weapons", since they do not appear on the weapons tables.
From the PHB, "an improvised weapon is similar to an actual weapon".
If you search this site for "improvised weapon" there are many answers about features that don't work with improvised weapons (warlock pact weapons, magic weapon spell, etc).
This is answered well in Are Improvised Weapons used in melee actually melee weapons? with the quote "Improvised Weapons are not a subset of Melee or Ranged Weapons, but they are Weapons."
See also What is the difference between a "ranged attack" and a "ranged weapon attack"?.