No such thing as a layover. It's either a connection, a stopover or nothing. OP has a "nothing." BA will check his bag to the final destination on the BA ticket, e.g. LHR.

Two hours is a ridiculously short period of time on separate tickets even if OP has no luggage. If there is a delay on the inbound, OP will have no showed for his DL flight and his DL ticket will be cancelled. Getting that ticket reinstated (presuming that it is a discounted penalty fare) will mean anything from paying a fee + fare difference to buying an entirely new ticket (as the return will have been cancelled too).

This one is simple. Don't even think of it.