Your forts have weird architecture. To get in a thirst loop described, average dwarf would need to walk at least 22000 / 10 / 2 = 1100 tiles. For contrast, 1×16 is only 768 tiles.
That's still a lot of tiles, so I'd also make your civilians "recruits" so they can carry at least some of their own booze, and maybe some food.
Anyway, regarding booze and minecarts - track stops don't seem to work, but unloading manually (give to order) seems to work. Booze inside minecarts can't be drunk, but raw food in cart can be eaten, so you can just have food cart moved along build side.
For acceleration, a minecart ridden/pushed on flat track can move 200ish tiles before coming to complete stop I guess? So it's mostly not necessary. Heck, you can ride a minecart over rough floor even with route stops every dozen tiles. If acceleration was necessary, I'd use two opposing T-shaped track/ramps for bidirectional acceleration.
For that picture, there's fair few options. I think roller toggling like PatrikLundell describes would be ideal (and I've seen people using that method - but it's not usually used due extra costs; you might even need to rebuild your powertrain here if windmill sits directly on top of that gear assembly), but you could also use a cart jump over the roller with rough floor+hole combination, or a L-shaped corner turn that takes it past a roller on return trip.
This means, for example, that the following tracks, when a (non-guided) cart travels from West-to-East, are functionally identical in effect:
A════════════B A╬║╚╔╣╩╦╠╥╨╞╡B
^ That means you can replace T-junction with L-corner turn.
Additionally, if you're just dumping goods and returning, there's the ?-shaped turns:
╔╗
╚╚═════