What should I prepare for traveling to Thailand on a 60-day tourist visa and switching to an education visa for my son?

If you applied for a Single Entry Tourist Visa you had to show onward travel, so why you not use the same ticket when asked?

𝟭. 𝗜𝗳 𝗶 𝗵𝗮𝘃𝗲 𝗮 𝟲𝟬 𝗱𝗮𝘆 𝘃𝗶𝘀𝗮- 𝗶𝘀 𝗶𝘁 𝗹𝗶𝗸𝗲𝗹𝘆 𝘁𝗵𝗲 𝗮𝗶𝗿𝗹𝗶𝗻𝗲 𝘄𝗶𝗹𝗹 𝗮𝘀𝗸 𝗳𝗼𝗿 𝗺𝘆 𝗳𝗼𝗿𝘄𝗮𝗿𝗱 𝘁𝗶𝗰𝗸𝗲𝘁?

that is between you and your air carrier, SOME do require proof of onward travel (even when you hold a valid visa to thailand) some do not CHECK with them

𝟮. 𝗜𝘀 𝗶𝘁 𝗹𝗶𝗸𝗲𝗹𝘆 𝗶𝗺𝗺𝗶𝗴𝗿𝗮𝘁𝗶𝗼𝗻 𝘄𝗶𝗹𝗹 𝗾𝘂𝗲𝘀𝘁𝗶𝗼𝗻 𝘂𝘀?

highly unlikely immigrations at passport control will say anything to you at all when you stamp in

𝟯. 𝗛𝗼𝘄 𝗲𝗮𝘀𝘆 𝗶𝘀 𝗶𝘁 𝘁𝗼 𝘀𝘄𝗶𝘁𝗰𝗵 𝘁𝗼 𝘁𝗵𝗲 𝗲𝗱𝘂𝗰𝗮𝘁𝗶𝗼𝗻 𝘃𝗶𝘀𝗮 𝘄𝗵𝗶𝗹𝗲 𝗶𝗻 𝘁𝗵𝗲 𝗰𝗼𝘂𝗻𝘁𝗿𝘆?

Not hard at all IF you have the correct documentation AND your child has enough time left on their entry stamp to do the in country conversion at the immigration office for 2000baht

You need to be talking to the school to see their time line to get the paperwork and check with your immigration office where you live to see how much time you need on your child's entry stamp to apply for the visa (because of the under review period the visa goes thru which is between 2 and 3 weeks depending on office)