There is a German page of 1&1 about installations of DNN 4.x:

http://hilfe-center.1und1.de/hosting/scripte_datenbanken/aspnet/16.html

It is easy to understand and only says that you should 

1. follow the installation process described elsewhere for the 3.x version
2. then update the connection string property in the web.config file as shown in the example.

Some more details...

1. You do not need to install the 3.x versions, just install the 4.3.4 version like they describe for the 3.x version (I created a small test domain on www.seychellensegeln.de with DNN 4.3.4).
2. So far, I just tried to install into the root (a copy of the DNN files into the root). I use subfolders for my other top-level domains (only static html pages and asp.net pages). They ask you to contact their support team if you would like to use a subfolder. I will try to do that as soon as I have some spare time...probably September.

My experience pretty much mirrors you as does my configuration.  After about an hour I it was trying to run the app  although it still isn't working.  so here's where I've gotten

After following the setup procedures outlined in another thread for installing in a sub folder on a Business MS package, I completed a sucessfull install of 1&1.  It did nothing for awhile (probably 1&1's servers updating or something) then I started giving me a generic servier error in '/' message.

I modified my web.config file so I could see the error, and got this:

Server Error in '/' Application.

---

Configuration Error

Description: An error occurred during the processing of a configuration file required to service this request. Please review the specific error details below and modify your configuration file appropriately.

Parser Error Message: It is an error to use a section registered as allowDefinition='MachineToApplication' beyond application level.  This error can be caused by a virtual directory not being configured as an application in IIS.

Source Error:

And it points out lines 54, 96, 151, 152