Does this mean that I could theoretically have my MP number in the reservation for flight benefits and status and at the same time earn miles to my bmi account?
Yes. FQTV is used for mileage credit, and FQTS for status benefits.
Would I earn MQMs in this situation? Would my flights "count" when they are considering people for GS?
I assume you mean lifetime miles? No. Lifetime miles (and I'm fairly certain GS qual) are based on FQTV.