Isn't it possible to override the tab layout for web AND mobile app?

The Salesforce1 mobile app is still pretty new,  but in our investigation we have had the same experience that you report.  It does not seem you can override the SForce1 standard nav elements with Skuid pages.  What you can do is create new visualforce tabs - populated with Skuid pages - and only include these tabs in your mobile navigation.  The following preliminary tutorial explains how to get started. 

 http://mobile.skuidify.com/s/mobile/m/14906/l/154279-showing-skuid-mobile-on-new-salesforce1-mobile-…

Well, the new layout is now also shown within the mobile app, but there is the problem, that the page isn’t shown entirely. The whole right side isn’t displayed on the screen. It looks like the web layout was directly transfered into the mobile layout, without adapting it to the mobile device. Any advice?

Ooo. Looks like you are using standard skuid pages on a mobile device.   These pages are not adaptive to the screen size of the device and so I would expect to see the behavior you describe.   

However, the mobile builder described in the link above is responsive.  Pages will adjust based on the window size. .  We rolled it out as Beta at Dreamforce in November.  It would be great to get some feedback from you regarding its performance.  Let us know what you are trying to get done. 

So, does this mean I have to create an extra mobile page for every page I want to be displayed within my salesforce mobile app? And do I have to use the skuid mobile builder for this?

We are still working on all of this… 

At this point we feel that the tasks your users will be undertaking will be different in the mobile environment than in the desktop environment.   This means we do think you should build different pages for your mobile app than you have for you desktop environment. 

You do not need to use the mobile builder to do this,  but recognize that pages built with the standard builder will not adjust responsively.  So you should build them “mobile first”  and probably do things like hide the header and sidebar from the get go. 

We’d love to get your feedback on how you think this should work?  Salesforce has taken the line that they will “automagically” convert your desktop views into a standard representation that is mobile optimzed.  We like that,  but do not assume that we know what all customers want in this sort of converesion, and so are trying to give more customization ability.  That of course means you have more setup to do.  Is it worth the tradeoff?   At leasts you are not writing custom code…   Again,  we’d love to get some feedback.  

I have used the Calendar component on a VF tab but on a phone it wont render at all… is there a problem with Calendars on the salesforce1 app?

Well… I wouldn’t say that the calendar component is mobile optimized at all. But I can get it to render within a VF page that has been added to mobile navigation in a SF 1 app.  (Using the tutorial I linked to above)

The week scheduling view looks viable - especially if you shrink things down to one or two days.   The day scheduling view does not look like it shows events.  We will have to look into that. 

What is it you are trying to achieve in the SF 1 environment?