Hi Michael,
1.The SID is different between source and target system , is it impacted by backup restore method ?
No impact on target system for SID. But post restore target system will have same client like source.
2. Our OS version is AIX and DB is Oracle, where I can find corresponding guide(step by step) for system copy using backup/restore method ?
You can use System copy guide available at SAP service Marketplace.
Additional help can be found here http://sapbasis.blog.com/2011/12/31/sap-with-oracle-homogeneous-system-copy/
3.Source client DB size is 3.0 T and target client OS free space only 0.9 T,
so do I need extend 2.1T space to the file system '/oracle/SID/sapdata' first ?
YES. Ensure Target system has similar storage space like source.
4. do I need use brtools to extend the data file of corresponding tablespace(eg: PSAPSID , PSAP700, PSAPUNDO....) ?
Just ensure enough storage space is available. During restoration no need to extend any tablespace.
Hope this helps.
Regards,
Deepak Kori