1) I am a newbie to Sencha Touch, and we need to build a cross platform mobile application
You need to start with sencha docs and start building some simple application.
Learn Sencha Class System
In sencha framework folder there is a examples folder you can find many examples there, use that to start leaning and experiment with it.
2) which involves upsync and downsync of quite a large amount of data through REST Web Services as background servies in Sencha Touch
Then, You need to know some more specific concepts like Store and MVC Pattern
If you are not familiar with MVC then
MVC in Depth Part 1
MVC in Depth Part 2
Useful SO link
3) if internet is not available data has to be stored in local sqlite db and after connecting to internet, data has to be synced
I think there are two ways
1, If your going to use PhoneGap (i am using it), You can do it by using PhoneGap connection feature to check internet is available or not, if not then there are ways to store data in local sqlite db in sencha.
2, I think sencha touch itself has device connection check feature (i didn't use it yet) to check internet availability and if not then as i mentioned above you can use local sqlite db.
So start trying and if you got stuck post here. you will get help from me and my fellow SO users.