Before I begin in responding to posts here I would like to say this is a relatively unexplored area of Warhammer 40k that deserves for attention. Not only for the sake of novels and Fluff but also because they contribute a key resource to the Imperium of Man; Manpower! In regards to the Imperium I feel they just need soldiers for their war machine, and wouldn't sweet the small stuff. However the Commissars might create a problem since they are aso strict on the R&R.
The Guard isn't exactly adverse to stepping on some toes (or necks!) to get their way.
No but sadly they feel they must play the Political game to keep favor with PDF, and also to build the Reputation of Guard commanders for career purposes.
I thought that the Munitorum or Administratum would enforce some kind of armor or uniform standard on feral and feudal regiments,
Unless it affects the Kill/Death ratio or drastically reduces their fighting ability the Munitorum would not touch anything. Again the Commissiarat might have a thing or two to say but it really would fall to the Unit's Commander for such a decision. Feral worlds would probably keep trophies and keepsakes; Uniform would only be altered by Fuedal worlds once the hand of the Imperium had been established for some time.
I feel like I'm answering my own question in a sense here, but would they be slapped with the same Flak armor and M35 M-Galaxy pattern lasgun that almost every other regiment receives or seems to receive, or is there an amount of leeway involved?
Probably, but if the soldier shows his adeptness at another weapon they may change that. I have only really heard of the Ratling Rifle and the blow Gun from the Tanith First and Only as exotic weapons origionating from Feral/Fuedal worlds.
How would a feral regiment handle tanks and other vehicles, and what kind of vehicles might be available to them, if any?
The months/years of training would drill that out of them; you don't give humans enuogh credit for their ability to adpat to new enviroments my freind. As far as tanks and vehicles are concerned I'm sure it would take awhile for them to learn how to operate/fight them. The Feral's would be the worst, as the Language/Communication barrier would be the worst.