Hello Vikash,
Firstly please refer this diagram for the process related to S/4 Migration
This shows how you can migrate from New GL to S/4 HANA and from Classic GL to S/4 HANA.
Note the dotted line which shows the migration to New GL ( Ledger & splitting etc) is a subsequent activity
If I may answer your questions piecemeal:-
SAP taken care of conversion of data related to New GL. Can someone please clarify?
Yes SAP will convert data, but this migration scenario is like scenario 1 for New GL migration ( read the New GL migration scenario)
It will not update document splitting characteristics or Other features of New GL
What happens, if client want to activate the Parallel ledger before we install S/4? Do we need to have SLO involved?
Yes you should
What if we activate the parallel ledger after the S/4 migration is done? How does SAP is going to handle? I have read some of the document that SAP will come with the approach to activate the Parallel ledger functionality...but when?
Answer to When is to wait 
, It may come next year in 1602 or may come this year in 1511
As shown above you need to perform all the steps of New GL migration after S/4 activation.
Hope this helps
Please close this thread.
Regards
Rishab