I also read a few stories that required the lender (Hard/Private Money) to show proof of funds and the lender didn't/couldn't. 

I invest out of state in apartment buildings, but I highly suggest that you do not invest out of state as a new investor unless you're investing in a syndication or crowd fund  or you're able to dedicate time in the market if things go wrong.

What is the cheapest and most reliable source of funding for real estate investing outside the normal FHA203K and Fannie Mae Homestyle Renovation?

A meeting was set up for me to sign docs, and briefly read docs as I was signing, the wire instructions were included.Just prior to wiring funds , there was a warning about wire fraud , and I noticed that no letter head was included with the wiring instructions.

As far as finding deals, have you picked up @Anson Young's book, Finding and Funding Deals?

@Madeline jI would continue to maximize your 403b contributions but keep in-mind that you generally won't be able to transfer those funds to an IRA until you either stop working for that employer or reach age 59 1/2. 

Would it be reasonable to expect to be able to raise rent with remodeling the units or is 400-475 pretty close to market rate for the area the multifamily is in?

Are you trying to raise the rent or get him out?

Additionally, most of them don't have the funds to actually market on their own so they use other people's leads.

@Tony MaticIf the funds are under the umbrella of a retirement plan, the loan will need to be non-recourse.