In Jomres I had different tabs like Tarrifs, Book now, Reviews etc. Now I installed Capella it only shows Property details and More Info. What did I do wrong?

Do you have the latest jomres version? (v4.7.0, as specified in the template description page)
If yes, then please make sure you also have the latest je_capella version (v2.2).

I bought Jomres and Capella just 3 month ago, should be the last version. Although it seems Capella is the v1.1. Is it posible to get an update for Capella?
Where can I look for Jomres' version?

Both Jomres and Capella are definitely not the latest versions.

First you have to upgrade Jomres to v.4.7.0.

To upgrade Capella (which starting v2.2 works only with Jomres v4.7.0), you have to download if from your jomres-extras.com account by clicking on My Account->My Invoices. Click on your invoice and at the bottom you`ll have the download link.

No, it is Jomres 4.7.0. But I can't install JE Capella because my support key is just no longer available since a view days. I thougth this support key was for Jomres updates and support only and not for third party software. Do I need to purchase an up to date support key just to install the latest version of Capella? Doesn't feel like fair.

I`m not sure what you`re trying to do exactly, but you should be able to install capella with no jomres support key needed. Just download the latest capella version, then go to jomres backend->plugin manager and install the template. That should be it.