I've only ever been asked by the airline, never at immigration. But as I'm sure someone will point put, depending on the mood of the specific immi officer on the day may decide to ask or may not, may decide to action, may not.... If I've ever had an issue at immi, I've managed to talk my way out of it. Really is pot luck
As I ivan said, its extra 30 days, the date you apply for the extension doesn't matter, the extension starts the day the visa exemption stamp would have expired. So irrespective of extension application date you will have have a full 60 days in Thailand.
Feel free for anyone to correct me, but I'm 99.9% you can apply for an extension any put after your first entry... it simply adds an extra 30 days to the end of you visa exempt date.