@Kacie Benson Most of your basic assumptions are right, but if you haven't already, I would really sit down (virtually, phone call) with a lender and model these out with real hard numbers. I just refi'd with @Chris Mason (no relationship, no stake in the game, met him on BP on Jan 29 and closed a refi a week ago) and recommend him for CA loans, he has a handy google sheet he can web share with you and walk through all the numbers and scenarios. Then plug into BP rental calculator to add all the other ongoing costs.
You can buy whatever first property you want, be it FHA house hack or rental prop in PS or triplex in Ohio. Really personal preference, and probably comes down to the best deal. In the last couple weeks I've made offers on everything from a small condo in PS (per our other thread) to a triplex to a russian river house to a ski condo. I would have taken which ever one gave me the best deal. None bit. I move on.
I am curious where in town here you plan to buy this mythical $350000 condo that could also warrant a $1000/mo room rent? Am I missing super cheap condos in Little Italy? I will buy 4 at that price! Also a $2435 payment I assume you are not adding insurance, utilities, capex, maintenance, etc. The average monthly cost will be higher. But as a house hack you do have benefits of tax write offs, mortgage pay down, and after 13 months capital gains exemption.
And where is this $180000 rental that can support consistent $1600/mo rent? (I assume Socal from your threads, harder to get close to 1% rule here). Maybe in downtown PS where you can walk to the ACE and Lulu's, but even that seems a little high. I would call 2-3 top rental prop managers in PS and take a poll. When I was in negotiation on the triplex I was not seeing market rent that high (although rentometer tried to say it was) based on real world feedback, and that was in prime PS. And if you are talking Palm Desert or Hemet, I really struggle to see that. And is that $1223 monthly payment counting HOA, insurance, any utilities, capex and maintenance reserves? IMO some of your numbers seem close, but at these small purchase points, being off by a couple hundred bucks can make the difference between somewhat profitable and in the red.
I am playing a bit of devils advocate here, to make sure you're tight on your numbers, and different folks have different views, just offering you mine. Go with the best deal first, and go from there. Don't look at it as "one or the other" in my view.
Lastly to your question of "Can you buy another property after using an FHA loan?" this is why my first recommendation is to talk at length with a lender. A lot of these answers depend on your income and DTI levels. If you make half a million a year, you can do a lot of things very fast because your statements and DTI limits are large. If you make $35k a year as a digital marketing rookie, your allowances will be much smaller. You have to pencil these all out with a lender, that is the sole person that can tell you firmly yes or no on these things.
"there might be a law against this? " not sure what this pertains to, nothing you wrote is against a law. Talk to a lender about your options on every scenario you are posing.
Good luck!