Claiming Spouse on H1b (Resident alien)

Hello,

 

I am a resident alien on H1-B status for filing taxes in the US.

I got married in Dec 2020 in India and my spouse came to the US in the middle of Jan 2021 an a student visa (F-1).  She wasn't in the US for the entire 2020.

 

So I have the below questions:

a) Should I file my taxes for 2020 as single or Married Filing Jointly?

b) If I need to file Married File Jointly; do I need to declare my spouse's India income in the US? [She is in the process of filing taxes in India since she worked in an organization till Dec 2020]

 

Please suggest.