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By applying pressure on the controls (or you’ve moved the mouse in your case), it will cause the autopilot to enter CWS mode. In Control Wheel Steering modes, the A/P will attempt to hold the pitch and roll that the yoke was last set for, even after the pressure’s been released. That’s what the “CWS-P” and “CWS-R” are telling you. If the sim is implemented correctly, the CMD button light should also go Off, and the CWS light should automatically be switched on to announce the current A/P mode. As long as movement/pressure are kept on the control, the A/P will remain in that particular (one or both) CWS mode. You need to somehow get the mouse to “release pressure” on the yoke before you can re-engage ALT or HDG (CMD mode).
For the A/P to follow the glidescope, the aircraft has to first intercept the G/S. And before it can intercept the G/S, it has to approach (get into range of) the G/S. You would want to approach the G/S from below, along the localizer. An unfilled diamond on the G/S tape indicates the aircraft is not in range. As you get into range, the G/S diamond will begin to move toward the middle. The diamond will turn solid magenta, that’s the time to hit the APP button to capture the G/S.
I do not know why the aircraft would continue to climb. Perhaps simply be a bug in the modeling of the particular aircraft (don’t know what you’re flying). I suspect that you may have already answered your own question—the high climb out speed. Mach 0.7 is rather excessive for the climb. Who knows, maybe that has induced some instability for the A/P?
The behavior and accuracy of the sim is largely dependent on the implementations for its flight model and autopilot etc. The default aircraft come with X-Plane typically are less developed. You should consider trying out the Zibo Mod B738. It is superior to the default B738 in every way. Though it will require more CPU & GPU power.
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