I’d first recommend exporting one or more of your clips into the HAP codec and seeing if the playback issue goes away.
If you want to use H.264 you’ll have to make sure that all of your clips have a key frame for every frame. If not, then your computer has to interpret the data and make a frame on the fly.
More on that here:
As for the output quality, what is your output composition resolution set to?
If you use a built in ISF shader is the quality better?
Please share photos or videos if you can.