No, RE stands for 'Regional Express'. There is RE between Hamburg and Bargteheide for example, but Berlin is too far away. REs are rather for commuters from nearby towns.

No you have to switch trains at least once.

Also the travel takes ~4h15m (RE->RE) instead of ~1h50m (ICE).

If your traveling at a time where the RE is not over crowded and you can spend the time well it's okay. If not, especially if the train is overcrowded in parts of the travel and it's really hot it's shit.

There used to be an IRE, which stands for inter-regio-express. But apparently it was discontinued during covid.