your employer should have all the documents for the company you are working for, what embassy is asking is the legitimacy of your employer company.....
NO, but logically something to support your stay in Thailand makes sense, if you say i get 200 or 400$ a month then they will think how will you support yourself....think how you would react if someone comes to you and ask you to stay in your house but not enough monthly income?
remote work means you are working so logically you are receiving money and you should have either payslip or payments from contracts coming to you, if you apply for soft power then they will not ask for payslips