i heard that with some numbers we omit de. True?
Yes, with numbers up to and including 19 (nouāspezece).
True. Without "de" up to nineteen. With "de" starting from twenty.
According to Wiktionary, cincizeci is pronounced (as well as sometimes spelled) as cinzeci. Could any native speakers confirm this for me? Vă mulțumesc.
That is correct. I'd say the pronunciation "cinzeci" is more common. We have short forms for a lot of numbers.
But are short forms of numbers used just in informal speech?
"de ani" has a drop-down translation which says "years old" as the default translation but is marked wrong. Can it mean "fifty years old"?
Yes. "Eu am cincizeci de ani" = I am fifty years old.