1) It is best to complete all of the wudhu in one place if it is possible.
If due to lack of space etc one has to move then it must be in the state that one is doing wudhu. So for example, to keep on wiping the arms, then coming out to do masah on head and feet.
2) just repeat the zikr correctly and continue with Namaz
3) just cover and continue
4) it is valid
5) it is valid
6) it is valid
If you did it accidentally you can do sajdah sahw at the end and Namaz doesn’t need to be repeated.
7) no it is valid
8) better to prepare before the time and have a place reserved in house for Namaz which is free from distractions and other things