your father might be acceptable, particularly as he's in Thailand. I think it definitely does matter, anyone can write a letter but family is less likely to abandon you if there's a call on the money
You can't. You need to be outside of Thailand to apply. Travel to the country you want to apply via, apply to the embassy in that country via the evisa system, and remain there until the process completes
Even though you own the Singapore entity for the purposes of the DTV you should have an employment contract that shows you are allowed to work remotely from Thailand
The risk is that your application gets cancelled. I've seen people being asked to supply copies of every page in their passport to ensure they haven't left the country, and others get asked to attend in person for an interview. Best to sit it out
You are on an extension of stay which means you signed a form saying you would notify immigration if your circumstances change. What is relevant is the date you will stop working, that is the date you need to cancel your work permit, inform immigration and leave the country. You can normally do this in advance with a letter from your employer then you will need to leave the country on that date. You can then return either visa exempt or with a tourist visa
You pay 500 baht per day but I'd avoid it if at all possible. If you come into contact with the police while on overstay you will potentially be arrested, transfered to immigration detention centre and deported
it's the passport that counts not where you currently live. And you're in luck as the Irish embassy provides income verification letters. You can read up about it on their website