Application for FlashDisk or Pen Drive

Question

Dear All,
 
I have a requirement to develop a application that will reside in a pen drive. User will open it using his PC without internet (offline backhand and Front app both will be inside pen drive)and Update his info whenever he want. Second he will have also an online account for it. he can update his info in online account. the application will synchronize the info between both online and offline database.
 
My question are?
 
1. As application in C#.net (i have to use) then could it run on Apple Mac, Linux and other platform? 
2. Application Must run with in Pen Drive. It will never installed any thing on User PC or Laptop. is it Possible?
3. Which Databases should i use for Both online and Offline Database which easily synchronized and compatible in Pen drive and on all platforms(Windows, Mac and Linux etc...).
 
Thanks in advance...