So, you have 8 gauge wire potentially subject to a fault current of up to 200 amps without anything tripping. You also have the neutral and ground bonded in a sub-panel (despite running separate neutral and ground wires to it, so bonding in the sub-panel is a puzzling choice in itself, as well as being a violation.) [or else possibly you have written unclearly about what you have done with the ground and neutral?]
Wrong. Just....wrong.
Pull two breakers, insert a 50 A breaker, and move the 15A circuits to the sub. And unbond/isolate the neutral and ground in the sub. Get a different/larger sub-panel if you need additional circuits (or give a long hard look at a complete panel replacement with adequate spaces in the main panel - not all that expensive if the incoming service is adequate, but attached to a panel with few spaces.)
If your panel is listed for them breakers with two separate 15A circuits in a single space breaker are another option to make space.
Correct. An Outbuilding needs a main shutoff switch even if it has one breaker. It does not need a main breaker, but it absolutely needs a shutoff switch.
It is unclear whether a "connected by roof" building is an outbuilding or not. Code plainly says it's not an outbuilding and does not need a main switch. Your local inspector is the final word on the subject.
Spend some time in the Eaton price book, and you find out that if you optimize for "cheap" or "compact", the best way to get a main shutoff switch is to get a panel with a big switch that by wild happenstance is a circuit breaker too. We don't care about that, we just need a shutoff switch. We only care that its "circuit breaker" trip value does not unnecessarily limit us. If your supply is 100A, then any main breaker 100A or larger will suffice.
This thing is not a breaker for us, and coordinating the breaker trip is hopeless - expecting this local breaker to trip first for our convenience violates Murphy's Law.
The one special characteristic this main "switch" might have is GFCI -- using an oversize hot tub panel is one way to provide necessary GFCI protection to every garage circuit at once, at the cheapest cost. The problem is, hot tub panels are woefully small, though this is helped by our ability to use double-stuff breakers if AFCI is not needed.
And "small panel" is death to a project like this. A person who brings 100A of service to their garage means to run some 240V loads. Those go through breaker spaces like congressmen through taxpayer dollars. Most loads in a garage need to be GFCI with some AFCI, so these will be full-space breakers.
The upshot is, don't even think of a panel less than 24-space...
Best Answer
As far as using the existing feeds to power a sub panel, no you can't. You can't parallel cables that small. The good news is, depending on the size of your conduit, you could pull some THHN in it, after removing the 2-12/2 cables. This could feed a sub panel and then you could reroute your two 120 Volt circuits into the sub panel and also add your 240 Volt outlet.