And yes, it is possible to defeat mother brain's 1st stage with just 10 missiles and 10 SMs (well, 9 actually).
Well, you can always beat the Metroids with Power Bombs, and refill at the ship. This'd be a major pain in the arse in this run, as you'd have to glitch into Tourian every time. If you DID do it, you'd only need the minimum of items, as you can do the Zebetite glitch, so you only need Missiles for the glass.