1) Can I use EIN to file 1099-NEC, and at the same time, keep using SSN in the 1099-MISC that property management company sends to me?
Yes. I do the same with my three rentals.
When you apply for the EIN you have to provide an SSN that EIN will be tied to. Only you and the IRS will know what SSN that EIN is tied to, and nobody else needs to know. So you'll be fine.
2) Which reason should I choose when I apply for an EIN?
Start at https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...
You can select sole proprietorship or single member LLC since both are considered disregarded entities by the IRS.
Also, do not lose this number once you get it, as it will remain tied to your SSN forever basically. Getting another EIN for the same business entity can be problematic at times.
