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I would do the polar alignment first and then do the star alignment.
Reason is if you do a star alignment and then do the polar alignment, the star alignment will be out after making the physical adjustments for the polar alignment.
Polar alignment is for the mount, star alignment is for the scope.
You should be able to get 30 second exposures unguided until you get a guiding setup.
The fact that the scope is moving in DEC and RA can point to not the best polar alignment. How did you actually do the polar alignment and how could you tell is was good?
The worm gear or whatever type you have is not that precise and can cause the jumps that cause star trails on short exposures. PEC can help with that. The scope is tracking, not guiding.
Limit your exposures to 30 seconds or less and see how you go. Take lots of them. No point going longer than about 30 seconds or you will have issues without guiding.
Cheers,
Damien.
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