Question about PCB layers
Well, it won't be "BOT" anymore :) (It would typically be known as MID or MID2).

In general, this should be alright. Keep in mind that it will make probing the signal layer considerably more difficult (you are limited to probing at vias).

Assuming a typical stackup where the middle planes are separated by a thick substrate, there really isn't much of a difference. You ought to have slightly better noise immunity and EMI shielding on the inner layer, though. You haven't specified what flavour of signals you are dealing with; as long as it's not too exotic, the effects of a change like this should be negligible.