I would try my luck and put no income (as that is the truth). If you do put income, they'll ask for payslips etc. If they ask for more documentation then you can write a letter explaining your situation eg you'll return to your home country after x months to look for work then return to Thailand. I would suspect writing remote work could make them think you'll work illegally in Thailand, unless you could prove that is what you already do in your career

Depends on the person assessing your application. My friend and I applied in hcmc for soft power (cooking). We both stated unemployed with no income bracket. I was approved within a week without further documentation requests, where as my friend was asked for proof of income. She wrote a letter stating she recently quit her job to travel for a while, submitted her tax return showing her income for the year and then approved.