Autopilot and Stab Trim Query

I read that the use of Manual Stab Trim (column switches) should trip off the A/P on a 737NG. It does on most Boeings, but, depending on what the A/P was doing at the time e.g. Autolanding, and the type of trim used, it may not. Does the NG trim have similar if's and's or but's?Does the NG have the old fashioned hand-driven Stab trim system... and would this trip off the A/P if used?Thanks.Cheers.Ian.P.S. Also, should I be able to, say, in cruise, switch from A/P A to A/P B simply by pushing A/P B switch. I thought it would have been necessary to disconnect A before pushing B? (Or is this not like other Boeings?)