1. It is false that operating systems of mobile devices can support full-scale software programs like Microsoft work or excel.
The mobile devices have limited screen size and that's why they can not support full-scale software programs, such as for example PC can.
2. It is true that mobile devices need to work within limited screen space. The major problem of the mobile devices is their limited amount of screen space. That is the reason why the design of the websites and mobile application depends on the screen size of the phone.