"tebrik" means congratulation, celebration. "Tebrik ederim" translates as "I congratulate you." whereas "tebrikler" translates as "congratulations", though both can be used interchangeably.
We do. Arabic numerals, advanced mathematics, waterproof architecture, the wheel, some my very distant ancestors who eventually ventured into Europe... we owe the Middle East a lot.
gözün aydın is not formal at all, actually it is informal. But you wouldn't say gözün aydın for something good that the person made, but for something good that happened to him. For example if someone they love visited them, or if they got a place in the university they wanted.
Where’s the stress in ‘ederim’? If I hover over the word, the stress is on the first syllable, but when I listen to the whole sentence, the stress is on the second syllable.