"I do not paint chairs."
Translation:Nem festek székeket.
You have a typo. "Festék", with an "é", is a noun meaning "paint". The paint that you buy in the store.
What you need is "festek", which means "I paint". A verb in the first person singular.
Other than that "Székeket nem festek" is also perfectly fine. The relation between "nem" and "festek" remained the same, you only moved the object in the front, making it more emphasized.
It definitely isn't. I recommend you to "pay attention to the accents", though, it's not a big deal nowadays to set a different keyboard layout. Some words overlap if you don't use them, also it matters a lot at pronunciation - so while we might be able to understand what you write, it makes your job harder if you ever want to pronounce words.