Nope. A mortgage is actually the piece of paper that gives a bank the right to take back your home if you fail to pay the home loan. A minor detail, but we're surprised how often "mortgage" and "home loan" are used interchangeably, when in fact they aren't the same thing. You don't truly pay off a mortgage - you pay off a home loan, which "voids" the mortgage at the end.
#2. My loan matures when my term ends.
You could be forgiven for thinking so, but not necessarily. The term of a loan is the length of time your lender uses to calculate your monthly payments. Most loans mature (that is, come due) at the end of their terms. An exception is a balloon loan. A 10-year balloon loan might have a term of 30 years (thus giving the buyer lower per month payments), but the loan itself matures at 10 years, which is when you must repay the balance in a lump sum.
#3. An APR is a neutral representation of how much a loan will cost me.
If only that were so! That was actually the initial idea behind "annual percentage rates", or APRs, which bundle together all the costs associated with your loan - interest, upfront closing costs, and other costs and fees - to tell you what your loan really costs you on an annual basis as a percentage. But you cannot use APRs to compare across loans for the best deal, because lenders don't all calculate their APRs the same way. Annoying, but true.
#4. The principal is the amount of my loan I'm paying down over time.
Sort of. But you won't be affecting the principal for a while, unfortunately. Most loans are designed such that for the first years, you are almost exclusively paying interest. Which feels a bit funny, since that makes the first few years in a home more like paying rent, technically speaking.
#5. You can choose which bank will hold your mortgage.
Alas, no again. One might think because you walked into the Bank of Money Bags that your mortgage therefore resides with them forever. But many banks immediately sell your mortgage to other lenders after they've made the deal with you. Which means an entirely different company might ultimately service your loan over time. The good news is they are bound to honor the terms that the original bank set forth.