Can I re-enter Thailand for another 30 days after using my visa exemption, and can I extend it?

Well before the 30 days expires, go ro immigration to extend for another 30 days for 1900 baht.

Here's an optional itinerary for a Laos trip you might really enjoy. Take the overnight vip bus to Chang Kong in the north on the Mekong river. In the morning when immigration opens cross into Laos, and take the two day slow boat to LuangPraBang, spending the night in Pak Bien, which is okay for the night. This trip gets very rural cruising down the river, with basic food and drink. LuangPraBang is a world heritage site. A few days there, out to the waterfall, and such. It has an interesting night market. From there take the day bus down to VangVien, on another river I can't remember the name of. After you get there you decide how long you want to stay. It is layed back with lots to do. From there to Vientiane, and cross back into Thailand. It's a nice way to be a tourist for a few weeks, giving you 30 more days visa exempt, plus 30 extension, and, you can do that once more with no problems. Or, you could just get a multi-entry tourist visa, METV, and stay here almost 9 months total, and crossing and coming back as many times as you want in the first 6 months it's valid for then crossing one last time a few days before it expires and come right back in, getting another 60 days+30 on the extension. But, you can only get the METV in your passport home country. Just a thought.

You can get two times a 30-Day visa exemption by land borders in one year. Unlimited by air - until the IO decides not to... Each 30-Day exemption can be extended by 30 days at IM.

You can extend your first 30 day visa free for another 30 days. Then cross border get another 30 days then extend that for another 30 days

All years except for the by air

You can extend any exempt stamp by 30 days

Yes, and yes, easy to extend, just visit your local immigration office, with passport, photos, TM30 and 1900Baht