...I have a 2m/70cm vertical with an MFJ window panel and G5RV on the way. My plan is to ground the antennas and the window panel outside the window with a ground rod and then run a cable around to the other side of the house connecting the antenna/station ground to the electrical service ground. Is this the right solution?
You're good so far...
Alternatively, the house is old and has BX wiring (flexible steel conduit) and good ground everywhere, can trying into this ground suffice for connecting to the electrical ground?
No, best not to do this. Keep your equipment ground separate and tie the station ground to the electrical ground at one place. Doing otherwise can lead to having ground loops which can be problematical to your station.
If I add another vertical or tower I would ground that at it's location and it's feedline would be grounded at the station entrance, yes?
If you put a ground rod at the tower or at the vertical, you'll also need to bond that ground rod to the other two, usually at the station ground outside the window. 73 and good luck!