UVA's Miller Center confirms that Melania Trump did begin modeling at 16, though it doesn't mention her doing so to support her family. This Today retrospective of her modeling career echoes this (and similarly fails to mention supporting her family).
Regarding the claim that she taught herself five languages, this appears to be unverified. Snopes conducted a fact-check and found the evidence to be shaky. According to their analysis:
"She has given a number of interviews and speeches in English due to her role as an American public figure, but we've found little evidence documenting her fluency in any languages outside of English and her mother tongue, and some evidence that casts doubt on her claims to multilingualism.
For example, when the Trumps visited Pope Francis in Rome in May 2017, a news clip captured the pontiff jokingly asking the first lady (in Italian) what she feeds her husband. The first lady didn't appear to understand the substance of the question until a translator repeated it in English."
Snopes found similarly little evidence that the former first lady could speak French or German proficiently, or that any languages she knew were self-taught.
The final part of the original claim is demonstrably false. According to the aforementioned Miller Center report, Melania met Donald Trump in 1998 at a New York City party, but she didn't become a U.S. citizen until 10 years later, in 2006 (one year after her marriage to Trump), as documented in both her White House biography and her profile on the Slovenia Embassy website.
Since the last component of the claim was framed as the most significant—asserting that Melania accomplished all these things before meeting Trump—the overall claim should be rated as false.
