after effects frame rates

Animation (keyframes) is always based on time. Changing the frame rate of a composition does not change the timing. Move a layer from 100, 100 to 400, 400 over 10 seconds in a 30 fps comp, then change the comp to 25 fps or even 120 fps and the move will still take 10 seconds. The only anomaly you may see when changing a comp from 30 fps to 25 fps is that the keyframes may not precisely line up at the start of a frame when you zoom into the timeline.

Change the file interpretation frame rate of source footage and you change the playback time. It does not sound like you did that. There should be no problems at all with the timing of your comp if you just changed the comp's frame rate. If there is footage involved you may end up with some blended frames but that can be fixed by trying different frame interpolation settings in the frame blending section of the timeline.

Entirely depends on what you mean by "slow". In fact you may already have worked against yourself. Since AE's evaluations are based on real time, there is no reason for sub-compositions and other stuff to be the same frame rate. As long as time is synced across al sub-comps AE will handle the conversion just fine and simply retime your keyframe. For footage source you will of course need time-remapping, using the Timewarp effect or simply re-interpreting the footage in the project window. Time-remapping could also be used to easily re-time pre-comps without actually moving a ton of keyframes inside them. Anyway, it's not really clear what you mean, but I suggest you look into these things. If you need more specific advise, more info will be required.

Mylenium