Marriage registration

There is no such necessity.  Once a marriage was registered, subsequent formalities are only formal religious rituals.  The same practice is being followed by those people who go abroad and obtain passports through regd marriages and formally undergo those ceremonies for visa purposes.

What is the status of previous marriage, i.e., it has been dissolved/ divorced or still subsisting ?

Anyhow it has to be disclosed for registration of this marriage if it is valid in accordance with personal laws (Hindu / Muslim / Christian etc.) governing the marriage.

It would be better to get the marriage registered.

Yes, now it is not required to get marriage registered again although you may undergo social formilities again.

If you want to please your parents,  you can simply get married again by performing traditional ritual if both side wish to celebrate that occasion. There is no need to get that traditional marriage registered again as it will be wrong under law. A marriage can only be registered once. But when you need to mention the date about when you got married in any official document, mention the date which is written in the Official Marriage certificate.

Yes, no further registration is required.

One registered marriage and another customary marriage ,no problem to register again .