What are the rules for extending a 30-day tourist visa and re-entering Thailand by land?

you need to go to the local immigration office where you are staying to apply extension of stay for additional 30 days. You cannot apply at airport. Most of immigration office allow you to apply extension 30 - 45days before your admitted until date so you can go immediately, but some allow you 15 days before. You don't have to (and shouldn't IMHO) wait until the last day.

You can get 30 days stamp on visa exempt entry at land order too, as long as it's within two times limit per year. And once you get stamped into the country for 30days, it's eligible to apply extension for 30days. Nothing different between visa exemption entry stamp once you enter the country by land or by air.

no - but at any immi office - not close due date / yes 30 / yes 30