Coiling coax doesn't harm the coax unless it's coiled too tightly. How tightly can you coil coax? Only way I know to say it is until you have to use any appreciable force in making the coil. Doesn't really tell you much, huh? Or, you might see what size the core is on the roll that coax came on. Another not too likely thingy, right? Oh well. A fairly good 'guestimate' is about a foot or so for average coax. If you're talking about 9913, or some really stiff coax, make that coil as large as you can. You can uncurl stuff like 9913 or hard line, but you ain't never going to get all the kinks out of it, make it easy on yourself.
A coaxial choke affects what's on the outside of the coax, not what's on the inside. And it does that in 'both' directions, to/from the antenna. So if you happen to have common mode currents (CMCs) on your feed line they aren't a bad thing to have. They affect things 'after' the choke, not 'before' the choke. That 'before' and 'after' thing depends on where that CMC originates, at the antenna, or at the transmitter. Which basically means put that choke as close to the antenna's feed point, or the output of the radio/amplifier/whatever as you can.
Chokes usually don't hurt anything. If they make a noticeable change, then there's something going on that you need to look into. Got some extra coax you didn't really need and didn't cut off? Coil the stuff up. Shouldn't make any difference. If it does, you got something going on that you need to be aware of. What? Beats me, I have no idea of what your set up is.
- 'Doc