How to remove door pull piece??
 

You need to pull the door panel to get that piece off. There's plenty of info on how the trim and panels come off floating around (I'm too lazy to dig it up right now)! :)

Pulling the door panel off isn't difficult. I've done it often enough in a year of ownership that it only takes a couple of minutes.

Removing X5 Door Panel, Replacing Window Regulator - YouTube
you can just slide it back and hang up clothes with a coat hanger

You shouldn't have to mess with the airbag for what you're doing. If you do have to get at something behind the airbag, just handle it gently and have some wire handy to hang it somewhere out of the way when it's unbolted.

A trim piece removal set is something you may want to consider. Although not necessary, it makes life easier....and theyre relatively inexpensive. Chances are, being an X5 owner, this won't be the last time youll find yourself removing the door panel! Lol.

Just a word of caution, the clip/light tube for the door handle light is easily broken when removing the door panel...so be aware of that, and try not to pull the door panel more than a few inches away until the light is unplugged. Pretty sure the guides have all this info though....

Lastly, you definitely do not need to worry about the airbag as removing it is not relevant unless you need access to the internals of the door structure (window regulator, door carrier etc.)

Edit: the paint "issue" you're seeing is actually the rubbery coating coming off the pull. I'd recommend just replacing it, not painting it. Since this isn't you're first bimmer rodeo, I'm sure you already know you can use realoem to identify the appropriate part numbers!