With the newest version 0.0.3027 I now can open my web app without errors when swiching to design mode :-))
There is however one problem and that is that I can select other pages on which I have put controls on.
Do you mean clicking on the tabs? You should use the properties in the Object Inspector to switch the page, still no support for such type of interactions with controls at design-time.
I tried to access the tabs via the Object inspector, but the first tab remains active. However, it works if you change the TabIndex property.
Yes, that is the expected behavior, still you cannot click on the tabs to change the active one, that is expected on the next release (1.1).