The post office is probably the most common place to go to get your passport. That's where I've gotten mine twice and my entire family of four have gotten theirs.

You take everything with you your form that you've had printed out and filled in, your passport photo, your proof of residency documentation, your other paperwork that is being required.

You don't pay online. You take everything that you need into a facility you give them what you printed out along with your picture and any other documentation that you might need. You pay then.

Check, card, or money order. Nothing that can be charged back as far as I'm aware.

To pay for the application and special services such as expediting your application:

Submit a check (personal, certified, cashier's, traveler's) or money order payable to "U.S. Department of State" Credit and debit cards are not accepted. Do not cancel your check or money order after you have applied. The acceptance facility will charge a separate $35 fee:

Money orders at all locations, payable as instructed by the facility Personal checks and cash (exact change only) at some locations Credit cards at U.S. postal facilities and some other locations. Note: the facility may add a surcharge to cover the cost of a credit card transaction.
Check with your acceptance facility to learn what form of payment they will accept before you apply.

If you're over at the age of 16 when you got your first passport then yes you need to do a renewal. You will bring in your old passport turn that in and they'll send you a new one.