@Riot Meddler, are you satisfied with the state of Varus in the modern game?
He was released in May 2012. Since then as an Immobile Poke/Catch champion who's core gameplay was Poke with Q, catch a squishy with R and deal mixed damage with Blight & Blight Detonation.
But right now his niche out outclassed by the likes of Kalista and even Ashe who can engage from a safer position and poke without having to put up with an absurd channel time that also slows an already immobile AD Carry. It's really not optimal because what you trade for that poke far outweighs the strength of the poke itself.
When I look at other AD Carries I seriously wonder why Varus was designed the way that he is. Does he really need a channel time on his Q? Should that channel time be as long as it is? Should channeling his Q really slow him? Sadly, the answer to most of these questions is something along the lines of 'back in 2012 it would be alright'. But since 2012 we've seen the introduction and rework of AD Carries such as Lucian, Tristana, Sivir, Twitch and Kalista who all have more Poke, Carry Potential and Mobility than Varus - even Kog'Maw got some love.
Now, I've played Varus a fair bit since I started playing mid-2012, and I've always liked his playstyle. But nowadays I can't afford to pick him in most situations because, despite my affinity for him, he's just straight-up outclassed in all of the roles that he half-fills. If I wanted a High-poke AD Carrry I'd probably pick Jinx or Caitlyn who are much safer and scale harder into the game. If I wanted a champion that I could use to initiate fights I would probably pick Ashe or Kalista who are also much safer where Ashe can engage from a much greater distance and Kalista is far more mobile.

running on mana... You would probably throw your PC into a wall after playing against him. Because he can SPAM SPAM SPAM (without following dumb energy regain antics) and all he has to do is occasionally back (which is unavoidable, I mean you can't win a 30 min game with just a Doran's) and buy a
.
?
ultimate or
either. Maybe increasing the slow on E at earlier levels or allowing for some synergy with his Q where if he hits an enemy on his E they're rooted or stunned?
. Both immobile, both have big teamfight ultimates. Here's where it changes. Jinx has longer AA range, her E is Hard CC as opposed to a mere slow, her Poke has a slow tacked onto it as well as it not having to be channeled, and she gets a massive movement speed boost on kill. Varus on the other hand gets attack speed on kill THAT JINX GETS FROM HER Q ANYWAY.