I thought after a year of being in my primary with a VA loan I could qualify for another VA and buy another primary and keep the other mortgage as a rental.

Yes you can as long as your father will live in the home as his primary residence and you put enough down to cover your portion of the loan that VA will not guarantee.Here are the VA guidelines for calculating the down payment.VA calculates the guaranty as described in the table below.Step Action1 Divide the total loan amount by the number of borrowers.2 Multiply the result by the number of veteran-borrowers who will beusing entitlement on the loan.There is usually only one veteran borrower, in which case the resultof this Step is the same as the result of Step 1.3 Calculate the maximum potential guaranty on the portion of the loanarrived at in Step 2 (as if that portion was the total loan).Use the maximum guaranty table in section 4 of chapter 3 of thishandbook.4 VA will guarantee the lesser of:• the maximum potential guaranty amount arrived at in Step 3, or• the combined available entitlement of all veteran-borrowers.5 VA makes a charge to the veteran-borrower’s available entitlementin the amount of the guaranty.If more than one veteran is involved, VA divides the entitlementcharge equally between them if possible.

My provisional strategy is to put a room in a property up for rent while also living in it as my primary residence for a year.

Or does it needs to be primary residence if we assume the loan 

Some want to acquire an asset in an area they enjoy visiting and are less focused on optimizing profit and others primary objective is to maximize returns.

In this case, should the series LLC be incorporated in my primary residence state with individual LLC’s in the respective states where my investment properties are based?

It only had one primary intersection.  

My question is, typically do banks lend on primary/investment properties with such a high price? 

Cash, developer financing, gaining citizenship, using a margin loan from an investment account or a heloc on your primary in the US, seller financing, etc. are usually the best options as bank financing with attractive rates and terms usually isn't available like we're used to in the US.

I have an opportunity that would eventually become our primary residence.