Hi Jacky and Chris,
I don't know of a Moodle activity designed from the ground up to do what you want, but it could probably be done with the Database activity or the Dataform plugin.
Database and Dataform both synchronize instantly as long as you have internet access. No Moodle plugins that I know of work in offline mode although some work is being done on making a Moodle version that can work like that.
Moodle, and all its various plugins, generally work very well on portable devices. I've personally used Moodle with laptops, tablets, and smart phones of all types. Some individual Moodle plugins may work differently or in a limited fashion due to the operating system of the device. My favorite portable device is the Microsoft Surface Pro 3 and 4 due to the really nice pen capability they have.