Is there a possibility to get the Create database, user etc. dialogs into Teradata Studio Express 15 the same way as they were (in Tools tab) in version 14.10? Or are they somewhere else?
If not, is version 14.10 able to access TD database version 15 and do the job? Is there a possibility to downgrade to version 14.10?
I think you are really asking about a change to Teradata Studio (not Studio Express). Studio was reworked in 15.0 to make many actions appear in the perspective they are appropriate to. There are three "Perspectives" that now have different actions available. The Create actions are in the Tools menu when the "Teradata Administrator" perspective is selected. They're not shown for the Query Development and Data Transfer perspecives.
Perspectives can be selected from the bar near the top of the window. Or you can choose one from the Open Perspective menu item in the Window menu..
Which version of Studio are you using. In Studio 15.11, the Create Database option is now part of the Object List Viewer. You will need to open the Administration Perspective and in the Navigator View, select the Connection Profile you wish to create the Database. Then double click on the Databases category in the Navigator. The list of Databases/users is displayed in the Object List Viewer. The toolbar will include a Create Database action. There is an article on DevX to help with the new administration UI (http://developer.teradata.com/tools/articles/new-teradata-studio-administration-user-experience).