By international, I mean no green card, no citizenship, no rights to work in the USA, and no social security number. 

Generally speaking, do not rely on Assessor's cards for assessed values, drive by the property, bring certified funds in incremental cashier's checks (any left over funds takes 2+ weeks to get returned), remember to pay taxes during redemption period, check municipal liens (demo/repair), determine your exit strategies.

So, to continue our example from above, if your mortgage payments with tax and insurance are $1,000 per month, you have a $250 car payment, $250 in credit card payments and a gross income of $4,000, your back end DTI is 37.5% ($1,500 / $4,000 = 37.5%).

The alternative options just so you know what cards are on the table are commercial loans on 1 or all 3 combined.

The title and property card says it a multi-family so do I need to get permits even though the property is said to be a multi-family? 

If you have worked with the contractor before and it is a easy material list, I do not see an issue with purchasing material and getting some credit card points.

If you start an LLC go get a business account with a bank and apply for business credit cards.

These added expense can be accounted for but that doesn't change the wild card of hoping your tenants don't ruin your leach field.

Obviously speak with lenders, your CPA and lawyer, but its very common for folks to start out owning residences themselves vs corporate entities, and just having some sort of liability insurance.If you do get an entity and what business credit, if I remember correctly you just need to register the entity with HMRC etc, and start out getting a credit card with whichever bank you choose to open a current account with.

My current card was issued in 2012..