So wait. If my total barter surplus is +3 does that mean if I roll in surplus at the beginning of the session I have 3 spending barter?
Yes. The barter you get is equal to your surplus.
And if so, if I choose not to spend it (as it's my personal cut of my hardholder) can I roll it over into the next session regardless of my next wealth roll?
No. It goes away if unspent.
Also a dumb question, what's the standard staring spending barter for a hardholder? Is it my starting surplus? Feels kinda low for a Warlord.
Yep, it's the surplus. And remember that Hardholders don't have living expenses at all, so it goes a bit further than it might seem. Plus they don't have to pay salaries to their gang or anything, basic expenses are deducted before you get to the surplus (so your actual income is more like 40-60 Barter, plus other expenses, plus your surplus...it's just that not paying your gang isn't really an option). And you actually have unlimited additional Barter for purposes of gifts to people you sleep with...
Really, Hardholders feel pretty rich in play. They never need to actually worry about money to live, and have some for incidentals when they want them, and can start with just about whatever gear they want. And actually, the fact that their Barter goes away every session makes them feel richer since they can spend it like there's no tomorrow. Only the Maestro'D feels richer (since they can get anything via 'Fingers in every pie'). Everyone else (except for Hocus, which feels similar to Hardholder in many ways) might have more Barter occasionally, but it goes quick so they feel the need to save it, not spend it. And that's what being rich is, the ability to spend money without worrying about it.
Also, a hardholder gets 40 violent bastards starting, so does that mean he has absolute command over others in the hardhold? Like if a hardhold has a population of 150 to 200 can he technically command them around, take barter from them, March them into combat, mass manipulate them?
He can command them (ie: force them to do what he wants like give him Barter) as much as his gang allows him to, though there will be repercussions. He can persuade them en masse if he has leverage (and he usually does, lets be honest)...but so can anyone else. Really, there's no limit other than logic to who you can Go Aggro on or Manipulate, regardless of playbook. A Hardholder using his gang as a weapon can Go Aggro on his citizens very effectively, and one who has things they want can Manipulate them.
He can't command the population as a whole with Leadership, though. Or use them as a weapon in battle or when Going Aggro. Those require a gang, and, well, they aren't one. They aren't an organized military force, heck a fair number are probably small children.