I have found a few multi-family properties I am interested in purchasing, all meeting at least my minimum cash flow numbers and Cash on Cash percentages, however these properties are about 4 hours away from my primary residence.

I have heard different things about conventional loans.What percentage down payment should I prepare for?

We have about half of the price of the building, but not the whole amount; we're also not excited about using all of our cash for purchasing, since we expected to put a percentage down on this one and be able to buy another building also. 

Worst case scenario, the company that bought at 70% (or whatever percentage purchase price made sense), can back it into a rental.So, if you don't want to acquire yourself directly from the seller, which is going to be one of the best ways to get deals, you are going to have to find and become the good wholesalers best friend.

I know there are stocks that beat that, but what percentage of stockholders have had the foresight and fortitude to hand on when the market tanks.  

If you're getting difficult tenants, then you can run into many, many problems and it's seriously not worth it the extra percentage on the cap rate you could get. 

This LLC will give/loan(not sure what the correct word is) money to my cousin's Company, and there will be an agreement to get a percentage of equity in the construction project(i.e each of the 6 investors may get an apartment after the construction project completes).

Basically you need to know the ARV of the new property, and calculate the percentage the bank will refinance.

I also added coin operated washer and dryer so didn't know if I should take out a percentage for that and not pass that on.

Even if they were brand new when she moved in, I would pro-rate using the three year lifetime and only charge her that percentage of your original cost.