How do the rules of vocal harmony apply to this sentence? In other words, why doesn't the indicator of plural accusative copy the vocal "ö" from the plural form of "mérnök"? Why is it not "öt"?
Vocal harmony in Hungarian usually is complicated and has many exceptions. The vowel harmony in Turkish is much more structured and logical
Yep, Turkish vowel harmony is pretty simple and the exceptions are few and easy to remember. Finnish vowel harmony is also simple.
Simply because you're not looking for certain engineers. Just engineers in General.
The translation of your sentence would involve an additional article (like in English), and the use of definite conjugation: "Én a mérnököket keresem."