There are several possible causes. The easiest to check and fix is that the holding tank is cracked and leaking. Its also possible that the needle is clogged up with grounds, you can use a paperclip to clean out the needle. It could also be that something is broken inside the which is difficult to diagnose without taking it entirely apart.

I've had this problem too when listening while my phone was charging. I unplugged the lightning cable and the popping went away.

If you go to System Preferences > Network > Wi-Fi, make sure that the "Show Wi-Fi status in menu bar" option is checked.

Yes it can be done safely. Here is a guide that shows how to do it: How To Fix Sticky Keyboard Keys on a MacBook

No, the most obvious reason is the different home button. The 5s has Touch ID and this changes the size of the button hole on the front face.