Can I - a visitor from abroad - rent a short-term accommodation while looking for an apartment?
Your main problem will be the short-term accommodation after arrival, since all hotels are closed to visitors.
Some form of cooperation with your future employer may be required to get an exception from the local health department for your initial stay in a hotel.
Is it still possible to visit apartments in person?
In theory yes.
When using real estate brokers, they will have to ensure that all contact rules are dealt with properly.
Is it feasible to proceed with necessary paperwork, i.e. register residency, open a bank account etc. or are opening hours severely limited?
To register residency, the online appointment fulfills the legal requirements, then it is a matter of waiting. Even before the pandemic, the waiting times were long.
My local bank still has normal opening hours where unavoidable personal contact is needed.
What about the actual move - are removal vans
As of 2021-01-11, professional transportation when moving is definitely allowed within Germany. It is their task to insure that local requirements (which may differ from state to state) are fullfilled.
Private assistance while moving (i.e. other private people helping while moving) is greatly restricted due to the 1 person outside your household rules.
Cross border moving conditions is not meantioned specifically.
Taking up residence is considered essential (at least for the immigration rules).
If you intend to drive yourself, you would have to have at least the electronic form which would state the address where you are staying after arrival.
A letter from your employer stating that you are
- taking up employment
- where you will be initially staying
would probably be useful to clarify any open questions when entering the country.
The present regulations have been extended until 2021-03-07.
What happens after that is anybody's guess.