H4 visa spouse: resident alien or non-resident alien

1. Yes, definitely.
2. For 2019, yes.
3. Well, her situation for 2019 is a little more complicated because it's her first year of residency. Since she is a resident by passing the Substantial Presence Test, her residency starting date is when she was first present in the US in 2019. So basically, she is dual-status for 2019 -- resident for the part of 2019 after she arrived, and non-resident for the part of 2019 before that.

You guys cannot use Nonresident Spouse Treated as Resident since neither of you was nonresident at the end of 2019. Rather, you can use Choosing Resident Alien Status. Both of those accomplish the same thing -- make both of you resident aliens for all of 2019 and allows (and requires) you to file jointly. Dual-status aliens cannot file jointly, so this choice is needed to file jointly.

So your options are:

1. File as Married Filing Separately, with you being resident for the whole year and she being dual-status. She probably doesn't need to file a return unless she has foreign income from the part of the year after she arrived. She doesn't need to get an ITIN if she doesn't need to file a return. You can write "NRA" in the space for her SSN/ITIN on your tax return. Married Filing Separately will almost certainly result in more income tax overall than Married Filing Jointly. Or
2. Use Choosing Resident Alien Status and file as Married Filing Jointly, with both of you being resident for the whole year. She would need to apply for an ITIN together with the tax filing. Making her resident for the whole year means her worldwide income the whole year needs to be reported on her US tax return, although she may be able to use the Foreign Earned Income Exclusion to exclude tax on her income from the part of the year before she arrived.

Another consideration is, if you didn't already get the stimulus check, then filing jointly with your spouse who doesn't have an SSN will disqualify both of you from getting the stimulus payment (at least under current law; don't know if it will change under an upcoming stimulus bill), whereas if you file separately, and your AGI when filing separately still qualifies for the stimulus payment, you might still get the stimulus payment.