You are not mentioning the most important point : What is the browser you are using on mobile ?
Local Storage, like the profiling, can be looked at through the debugger and should be likely used in preview over WIFI.
As far as I'm aware, the save/load system feature works the same on desktop browsers and mobile browsers, as long as the browser does support the HTML5 feature.
Congrats on building your game "quickly" and taking on C2 in a fast manner, but in terms of help request, nothing beats providing your actual project, or a precise reproduction of the issue in a simpler project (if you don't want/can't share the main project) with precise steps on how to reproduce the error in a consistent manner.
I made a tutorial not too long ago on how to use IAP and admob's official plugin and export it through Intel XDK, hopefully it answers your doubts about monetization.
C2 doesn't limit your game's performances, but be aware that mobiles do not share the same hardware as desktop, and if you end up feeding them too much/too big assets, they will choke and under perform. Just follow the performance tips, the memory usage tips and try often your game on the target device to make sure of the performances.
Finally, you mention online save, well you need to store your data on a server-side, using some server side script, and this is out of the scope of C2.
Google drive or an online file hosting system like that won't likely allow you to, for security measures on their end, allow anyone to write in a file hosted on one of their account.
Check the "How do I FAQ" for more infos on database/server-side but be aware this is out of the scope of our forums, since it depends on the language you use and the kind of server hosting you go for.
Nevertheless, the AJAX section can provide you with examples on how you may do it work.
On a moderation note, please don't bump your topics less than 24 hours prior to the last message you posted, especially during Christmas/holidays times.