pickin up a ball is only allowed on the green and that 1st and foremost reason is to clean the dirt and debris from it as that severly effects roll.....the only other time pickin up a ball is allowed is when excessive rain makes the fairway muddy....pick clean and place is allowed for the same reason as above
since the coin or marker on the green is allowed why not have a line on the ball to line the putt up ( I don’t mark my balls ) but it is helpful for most.
the flag stays in the hole til all players balls are on the green
I saw an incident (women pros) where one gal had a really long putt, they pulled the flag and then put it back in for two others that were on the first cut.