I’d love to explore the possibility of partnering with a fund or securing a credit line to expand my reach and find more clients.

With that being said, I am trying to find out if new construction is even possible and what it takes to build a small multifamily in the LA area. 

Yes, it's possible to get an FHA loan with 3.5% down in the city, but your lender is right—there are some tricky hurdles, especially for multi-units.

We have both been reading and researching as much as possible.

You don't want to overstretch on the first one.In terms of evaluating quality deals, you won't know what those are for a while so you want to get as many reps looking at properties as possible.

Are they doing everything possible to expose properties to the broadest possible market?

We are looking into the possibility of starting out OOS investing in Indianapolis.

I would then work to renovate the bad unit as quickly as possible.  

My plan is to take the next six months to try and learn as much as possible about multifamily real estate, while also saving up money to be able to start a career in brokerage.

Is it possible to avoid taxes on the gains if I buy another property for $564k ($900k - $336k) and make capital investments of $336k?