All you read is correct. None of your examples are actual ordinal numbers (first, second, third instead of one, two, three), which are indeed formed bei adding -(s)te: der erste der zweite, der dritte. You use these when you want to assign objects a place in a series: He won the first place = er gewann den ersten Platz. "50er" is just the plural: die fünfziger Jahre = the fifties, not: das fünfzigste Jahr = the fiftieth year. In a date, the year is given as a cardinal number, just as in English, not as an ordinal number (you don't say "it happened nineteen seventy-third"). So, it's basically just the same as in English.

Ordinal numbers are "first", "second", "third" and so on. They're not used for years - compare "the 1950s" or "in 1973" in English, not "in 1973rd" or so.