Hi Shree,
i am kicking in as my name was mentioned here 
>> 1) Once HA system built on RHEL cluster can we restore the archive logs from old production which is on AIX?
Depends on how you have taken the archive log backups. If you have not used RMAN and still got the archive logs in some third party backup tool, then yes you can restore them. However this does not make sense at all as archive logs can not be used for recovery in cross-endian scenarios like yours (AIX = big endian, Linux = little endian). The format is different.
>> 2) We are doing SAP export import method to build the HA system, So is it possible to apply archive logs?
No for two reasons. First the cross-endian scenario that i have mentioned before and second you get a completely new database on the Linux system if you use the SAP export/import method.
>> 3) Can we do data compression while exporting the data in source system?
The data itself is compressed by default with R3load, but i think you mean the Oracle index or advanced compression. And yes you can also enable the Oracle compression stuff, but this is done in the import phase, not in export phase.
>> Maybe Stefan Koehler can have better suggestions on this like using Oracle to Oracle
It all depends on your downtime requirements and the corresponding database size. However there is an advanced Oracle migration scenario called "Transportable Tablespace using Cross Platform Incremental Backup", which reduces the downtime to only a few minutes regardless the database size. This scenario was introduced for Exadata migrations only first, but luckily Oracle removed this restriction (more details can be found in MOS ID #1389592.1) and it works 
Regards
Stefan