My car is a semi-daily driver. (It's more than a weekend toy, but I probably only drive it to work once or twice a week.) I do use it a lot for running errands with my kids or the whole family in tow. You can use that to weight my comments accordingly.
I'm about 1/2" over 6' with a 33" inseam, and I fit just fine with a helmet in a non-sunroof/manual seat car. The sunroof and the power seats will both eat headroom. However, fitting in the car depends more on torso length than total height. Even with my long-ish legs, I drive with the seat two or three clicks forward.
My kids (4yo and 1yo) are smaller than the OP's, but the back is fine for them. My full-grown coworkers don't mind riding to lunch back there, but I doubt any of them would want to go on a road trip that way.
My car burns so little oil in street driving as to be a non-issue. It burns maybe a quart in 3k miles. Track use (HPDE) is another matter entirely. I'd estimate that it burns around half a quart per hour of track time. If I start with a full tank of gas and a full crankcase, it will need gas before it needs oil, though I usually fill both at the same time. Other guys at the track seem to have less oil consumption than that.
The gas mileage is not great, but if you drive the car sedately it's possible to get much better than what most report. Driving carefully I get 24mpg on road trips and about 20 in town (on pretty sticky Dunlop Z1s). Driving what I consider "normally" (probably still slightly sedate), I get about 22 hwy and 18-19 in town. On track I get around 8mpg. The key to getting good mileage is not revving the engine into oblivion when you don't need to. I typically shift just under 3k when driving sedately.
We don't get much snow in Houston, but I think it would be just fine, especially with snow tires. If you're really worried about it, look for a model with DSC (stability control). The DSC program is pretty good. It's substantially less intrusive than the ASC on my E36 M3 was, and can be switched off for track use. (Unless you're trying to set a lap record, you can leave it on during track use. It will let you slide the car and/or step the tail out slightly if you're smooth about it.)