Discounted economy earns 50% on bmi flights, and the Silver bonus is just 25%, so you will earn 313 miles and 10 tier points for the Manchester-Heathrow leg on bmi. Your BA Silver will grant you access to the bmi lounge at Manchester.

SAS operates from terminal 3 at Heathrow, so you will not have access to any of the T1 lounges. Even if they did operate from T1, however, you would still not be able to access a bmi lounge with a SAS boarding pass, even though your flight was booked with a BD code, as bmi has now left Star Alliance and all *A benefits ended on 31st May.

However, your TAM *G will get you access to the SAS lounge at Terminal 3. You cannot earn BA miles or tier points on the SAS leg, but you will be able to credit those flights to TAM.

If you're returning by the same routing, use *G for miles and status-related benefits on the SAS leg, and your BA Silver on the bmi leg.