We want to take a BACKUP of our data in Teradata and
RESTORE it on another Teradata box. Is this possible, and if yes do we neeed to have same version of database on other teradata box? What are the tools available for this?
RESTORE it on Teradata Emulator perhaps running on Windows/Linux box. Is this possible, if not entirely at least few tables?
Yes, you can. Make sure that system you're restoring backup to is the same version or higher. Most basic tool you can use - "arc" also known as arcmain. It is part of Teradata Tools and Utilities pack. But make sure you're using for restore very same version of ARC as you were using for backup. More advansed tools are: DSU from Teradata (or ABU in older versions), NetBackup from Symantec.
If by Emulator you mean Teradata VM - yes, again possible with same conditions mentioned in #1.
Not by backup-restore. It would be more export-import operation rather than backup-restore. And you need to use custom tools for it.
Same as #3. There is a tool called Teradata Connector for Hadoop that can help you with data movement between Teradata and Hadoop.