There are 3 things legally required for entering Thailand as a tourist:
1) Proof of funds - 20,000 baht or equivalent in another major currency IN CASH ONLY (no credit cards, no bank statements, no bank apps)
2) Proof of onward travel - a ticket out of Thailand within the number of days you will receive on arrival
3) Proof of lodging - a few days hotel reservation at a minimum
The only time immigration ever asks for any of these is if they are looking for a reason to deny entry to you. So if you don't have a long and extensive history of entering Thailand or any sketchy visas in your past, you should be fine.
Your airline is far more likely to require proof of onward travel before they let you checkin to your flight though.
Visa exempt is a 60 day stamp every time you enter without a visa. You can do it until they say you can't. There is no limit written into law, but each entry is at the discretion of the immigration officer you are standing in front of.
because applying online doesn't change that you must apply with the Thai embassy where you physically are. They will require you to prove that you are in the country as part of your application.
that's all correct except you cannot apply in person in Malaysia anymore. They have switched to e-visa so you would travel to Malaysia then apply for your visa through the e-visa website, choosing the consulate that you want to process your application. The only SE Asia embassy that still accepts in person applications are in Laos and they require an appointment.
You need to ask your airline what their policy is for people that are traveling to Thailand without a visa. They are the ones that might give you problems.