"is it possible to have internet in both my old place and my new one for a brief period of time? "
I wouldnt bet on that.
"I noticed that some of your customers lamented delays in the actual starting date."
Yes that can happen. Example: You move but the cable in the new house are missing - issue.
"Would it be safer to activate a new contract in the new home and, once it is active, delete the old contract in the old home?"
Depends - There will be minimum contract periods.
When your old contract is out of it and has a one month cancellation period - why not.
But you are playing with fire - because someone somehow just has to mess it up and its party time with costumer support - and a lack of german can be a problem.
"Or is there a portable solution that I can rent as Hotspot, just to have some security wile the actual transfer of your service takes place?"
VF doesnt act pro active.
Get yourself a prepaid card and a hotspot - you can use it later as backup solution - but before check the network coverage.
