I'll have to do some checking, but it's possible they weren't able to pressurize the B-29 (or was it the B-29's big brother, the B-50?) while the X-1 was hanging underneath. Then again, the B-29/50's bomb bay was never pressurized.

Unlike the experimental planes carried under the wing of a B-52 (e.g. X-15, X-24), the X-1 pilots got on board the plane while in flight. If he rode up in the cockpit, then they would've had to depressurize the plane before he could leave. I'll see if I can find out where the X-1 pilot sat while they climbed to altitude.

The name I always heard when I was doing space intel was Tyuratam, not Balkinor. I don't when the name changed, perhaps after the fall of the Soviet Union. Actually, according to this source, the Russians called it Baikonur after a village 500 kilometers away as part of a disinformation campaign.

As for the Atlas failures, there were a bunch of them. Yes, many of those shown in TRS were stock footage from the ICBM tests. However, quite a few of the Atlas space boosters apparently failed, too, including Mercury-Atlas 1.