Some were unwilling to provide proof of funds.

This means building a budget that includes setting aside funds for your next investment.

And then monthly by check or if you don’t trust them certified funds or EFT. 

These investments may be better than a mutual fund, but REITs miss most of the biggest benefits of owning real estate.

If raising all cash would be my primary method for funding these apartment deals, what would be your guys contingency in order from most preferred to least preferred. 

Second link is a similar size, albeit 10 year older home, in Setagaya Ward (a very desirable neighborhood), but still "only $1.2M. https://www.homes.co.jp/kodate...https://www.homes.co.jp/kodate...(2) Age. 

This is some of the most desirable and difficult to develop real estate in the country, owned and operated by many of the most powerful and affluent individuals and corporations on earth.

If your first home cash flows well as a rental, consider keeping it and using a BRRRR strategy, cash-out refinance, or HELOC to fund your next deal instead of selling too quickly.

First question: how much cash do you have to invest, and is this separate from your emergency funds? 

May be you meant that the IRA has deferred-tax funds and not Roth?