If you have a lien on your vehicle you may have issues getting a permit for it. They will ask for a letter of permission from the lender to take it into Mexico.
1) The lender may or may not give you permission. You may use either Registration or Title. If a lien does not show on one of those, you can play ignorant and get away with it. Your choice, but make sure you have the units covered fully by Mexican Insurance.
2) Most of our customers are retired. That usually means having your house paid off. Consider taking out a line of credit against it with a bank. Most banks will do this at no charge. Interest rates are usually low and you only make payments if you use it. Otherwise it just sits there and is just one more thing you have to clear, if you sell. One advantage is it can make it a lot harder for someone to do title theft against you. Use that to pay off your loan and make payments there instead, the bank will not care if you take it into Mexico.
If you have Residente Permanente Status in Mexico, there is no way you can get a permit. You can only take a Baja trip. If you have Residente Temporal that is OK, or if you are a Mexican citizen with a foreign passport or permanent resident card as well.