Regarding mortgage interest, is a Timeshare consider second home/vacation home or Primary home?

Yes, it can be. if it is deeded and recorded in public records and it meets all the requirements for deducting mortgage interest.

If you rent out the timeshare during the year, you must also use it as a home for more than 14 days or more than 10% of the number of days it is rented. You count your days of use and the days of rental only during the time you have a right to use it or to receive any benefits from its rental.

Mortgage interest can only be claimed on a maximum of two homes (main home and a second home). If you have mortgages on two homes and a timeshare, you won’t be able to deduct the mortgage interest on one of those properties.   See - Timeshare