Will my DTV request be rejected if I apply from a country other than my employment origin?

In fact, it's probably better to apply in countries outside of where your employment is based in case they impose strange requirements like extra documentation related to your work, for instance in Myanmar, they're asking for proof of registration with government authorities or something to that effect, which is not something many people can prove. An applicant working for a Burmese entity but applying in Laos or Vietnam won't be asked for such documentation and thus has a higher chance of success.

No.

No

I was worried about this too but its fine

Im uk passport holder, south korea resident and i did my application in Laos

No. You just can't be in Thailand when you apply. Plenty of people work for companies based their home country (or elsewhere), but apply from countries outside of where the company is.