Does my foreign spouse need to file Fbar on her own if her foreign bank account has more than 10k USD (we file jointly for US tax return)?

Me: US permanent resident

My wife: Lives and works in a different country, no immigration status in the US, already applied and got ITIN

We will file jointly on the US tax return.

We do not own any joint account in the foreign country. She has her own bank account in the foreign country, and I have my own.

 

Questions:

1. If she has > 10k USD in her bank account in the foreign country, does she need to file Fbar on her own?

I am guessing the answer depends on if she is a US person from the tax perspective (?!) Will filing tax return jointly or owning the ITIN make her become a US person so that she needs to file Fbar?

2. If the answer is yes for 1, she and I will file Fbar separately even we will file jointly on tax return, right? 

Thank you all for the help!