solution?

I have another question.

Can we rebuild all index online? I mean run this process on live/production database?  it is true that certain version of MS  SQL server like enterprise 2008 above can do it? it will not lock out the tables for accessing when doing this kind rebuilding?

your links do not say the Online index operations are available only in SQL Server Enterprise, Developer, and Evaluation editions.

But, I want to do index rebuilding for all indexes Simultaneously/Parallel.
Then you will have to open multiple connections and run the rebuild separately.  There is no other way.

You should consider why you are rebuilding all your indexes and not just the ones that are fragmented.

We have large amount of index fragmentation. Even we do defrag them, it takes a long time - 1 days to complete. I think, if we can do parallel, it will probably reduce the process time.

My point was that regardless of whether you do it in parallel or not, you should only re-index/re-organize those tables that are fragmented, by whatever measure you deem.  But quite honestly you probably won't save much time doing it in parallel and probably your biggest problem will be your Transaction Log growing very big, very fast.

if so, the question is how to reduce the transaction log? Do you have website support you say " won't save much time doing it in parallel "?

if so, the question is how to reduce the transaction log?
Actually the question should be how do I prevent the Transaction Log from growing?  And the answer is when using Full Recovery Model backup the Transaction Log more frequently.

Do you have website support you say " won't save much time doing it in parallel "?
I am afraid not.

my database is simple recovery mode

my database is simple recovery mode
Than you don't have to worry about Transaction Log backups and just make sure the Transaction Log is large enough for your situation.