Yes, if your partnership remains intact (how you sell is how you have to buy), and you structure it is tenants in common with the new ownership on the replacement properties. 

If I were you, I will buy a house with cosmetic work and learn the business first. 

Just bought my first buy and hold in Ferndale Michigan and it is turning out to be the best decision I could have made.

You might be asking the wrong questions at Fidelity (not sure if they do or do not allow this), but you aren't technically investing directly in real estate, you are investing in private equity partnerships that are investing in real estate.They might not want you buying direct interests in real estate, but are okay with private equity investments.

Buying without any skin in the game is high-risk and a recipe for disaster.

I’m currently looking to buy my next primary residence to house hack.

I've done flips, BRRRRs and buy and hold in the LTR  and MTR spaces.

I think the only way around that *may* be to go to something along the lines of a UPS Store and rent a PO Box that is listed as a Suite address (so instead of PO Box 1234, it's 1234 Main St, Suite 10). 

You are not allowed to assign if you are buying at auction

I learned about property values when I was looking to buy them to fix and flip.