1) Yes, it happens all the time. Incrementally, improvements become harder and harder to make the more proficient you become. Getting from 0 to 30 isn't that hard. Getting from 30 to 45 is harder. Getting from 45 to 60 is harder still. Getting from 60 to 75 to 90 really pushes you (to new levels of frustration if nothing else).
2) The E string is generally open. So make sure all your 'fretted' strings are pressed down firmly. If you don't have solid calluses yet, that's part of the problem. If you do, make sure you've got your fingers as close to the fret as possible, pressed down solid, but not enough for the note to go sharp, etc... Another thing to check is that your E string is in tune. Out of tune notes always stand out.
3) Check where you are picking/strumming. You may be moving your picking hand up toward the neck, which has the result of you shifting the guitar to the right. Also make sure your body is straight and square - you're not twisting at the waist trying to read music or anything else that would put your right leg in a different spot relative to your shoulders.
Try 'anchoring' either your forearm on the 'heel' of the guitar or a finger on the pickguard and see if that helps.