I think the course corrections are so tiny at our human body scale that one wouldn't notice the corrections. People sway side-to-side as they walk constantly. At high speed one might notice the changes, but again, the controls are constantly adjusting in all directions. I'd conclude it's hard to detect since nothing moves in a perfect, linear way.

Yes. According to what is agreed upon by most flat earthers, you would need to circumnavigate by diligently correcting your course according to the compass and/or stars. I'm no sailor, but to use a compass, you would sail by keeping the magnetic north port side (Left side when at the aft of the ship and facing forward.). Shamefully, I am no astronomer, but someone with an intimate knowledge of the stars and their courses could navigate using their positions in the night sky according to the time of year, much in the same manner. (Obviously, the navigator would have to make corrections around obstacles/land.)