Question: What is PITI?

Answer: PITI is the mortgage payment. You can think of it as a list including principle, interest, taxes, and insurance. Those are the components of most mortgage payments.
Principle - You borrowed money and every month you pay some of it back. The money that goes to principle reduces how much money you owe. It's how you pay down your mortgage.
Interest - It costs money to borrow money so every month you pay the lender for the use of that money. Whether or not that interest rate changes or how it is amortized was all spelled out in the beginning, before you completed the loan agreement by closing on the property. Amortized refers to how long it would take you to pay off the loan by making regular monthly payments. Most mortgages now are amortized over 30 years.
Taxes - Your lender will want to make sure the taxes are paid on the property - mainly because a tax lien would take precedence over a mortgage. This means if you did not pay your taxes and your mortgage, the taxes would be paid first in a procedure against you. The lender will collect from you monthly and pay your quarterly tax bills.
Insurance - This refers to one, possibly two, types of insurance. First, the lender wants to know that your property is insured. For a single or multi-unit building, the owner will have hazard (also known as homeowner's) insurance. A buyer will secure one year's insurance prior to the closing. The lender will collect monthly to make sure that when the bill is due again, they can pay it. For a condo, the insurance is the master insurance paid through the condo fee. A lender may also require HO6 or interior insurance. That would be handled much like the insurance on a single family or multi unit home.
Also, the lender may have required that the loan be insured. If  a buyer's down payment is less than 20% of the purchase price they will have to pay mortgage insurance or do a loan program that addresses the situation otherwise. This is often called private mortgage insurance, or PMI, but actually that is the name of a company that offered it. It is correctly called mortgage insurance or MI. If you are paying mortgage insurance it will part of your mortgage payment. 

Question: There are two of us buying together. Which credit score will the bank use?

When people ask this they are usually hoping that the answer will be in their favor. They want to know if the lender will average the scores or use just one? They would like to hear the lender will use the higher one or even the highest possible one.

Everyone has three credit scores, one from each of the three major credit reporting bureaus: Experian, TransUnion, and Equifax. The lender will take the middle score that each person has, not the average, but the one in the middle of the three. Now each person has one credit score and the lender will take the lower of the two. 

So if Borrower A has three scores – 680, 700, and 710 – and Borrower B has three scores – 820, 780, and 800, the lender will have 700 for Borrower A and 800 for Borrower B. The credit score used for the joint mortgage application will be 700, because it is the lower of the two middle scores. 

Sometimes if one of the borrowers has a very low score, the other borrower might try to buy alone. This can only work if that borrower can support the mortgage on their own income. If the lender is not taking into consideration a borrower’s score, the lender won’t use the income either.