Should I Replace Bx with Romex?

BX relies on the armor for the ground. Yes you can pig tail any wires that are too short in a box. Yes romex can be use as a replacement and I recommend it if you have access, It must be sized according to the size of the breaker 15a=#14 20a=#12. so the new romex to the box needs to be grounded in the box.

Is BX safer than Romex?

Romex cables are light and have a slippery coating that enables them to be easily pulled through holes. BX cables are safer and protect against any accidental penetrations. Romex cables have vinyl sheathing that you can penetrate easily.

Can you use Romex with BX?

BX would not be require to be run in metal conduit as long as it followed the building surface, the Romex would. You should be able to attach the conduit to the wall using the proper fasteners and anchors (if needed). If it is concrete you will need to use a hammer drill.