Red PEX is curling or bowing throughout the main hot water line from hot water tank feeding all the faucets and showers. Is this normal?
It is most likely fine. As others have pointed out, PEX comes coiled and it is completely acceptable to have it installed with curves and arcs, like this:
PEX is not like copper or iron pipe. Rigid pipe is... well... rigid, so we get used to thinking of plumbing as begin built from straight sections, but that isn't the case with PEX. I'm assuming the installation you are looking at is otherwise properly installed and supported, and the only part that has you concerned are some wide bends/curves. If that is correct, it's completely normal.