Why computer IDE run offline and mobile IDE run always online?

Answer 1

I think as no internet connectivity and in that case for sure you can work offline unless you're using some APIs that need internet connectivity and you cannot...
Mobile IDE cannot run offline because most importantly it can not supports all kinds of CPU architecture (x86,ARM,MIPS) ,as recently some of the new tablets have Intel Chips.

Answer 2

I have just used QPython3 offline. It works, I can use the console and edit and run files.

Answer 3

Code is stored server-side. It is compiled and run server-side, too. How would you save your code offline, thus? This is a cloud service. Only web code is rendered by your phone.

You can install compilers/interpreters and IDEs for many languages from Google Play and store code locally if you prefer.