Newborn in the space lookin' for some information...

I'm hesitant to buy BTC since my residency is always changing. I'm originally from the USA, but work currently has me place in Germany. My plan is to purchase a decent fraction of BTC here in Germany to get me started, and then when I move to my next location by next summer really start my investments. Will fiat to crypto exchanges such as Coinbase or Kraken accept me despite the fact I'm not a permanent resident in Germany? Will the currencies i purchase be able to move with me? Is it possible to take currencies from exhanges to cold storage directly, or would i have to use a desktop wallet, such as Exodus, as a "Middle Man" to store them?

Thank you for your time!