What is the significance of the ' (apostrophe) in deadline'm?
The apostrophe is unecessary here. It should be "deadlinem".
When foreign names or words are used in Polish sentences, they usually get declined just like Polish words. Apostrophe is used when the word is ending with a vowel and the declension ending begins with a vowel too - then the apostrophe comes between the two vowels.
So it's: Snoopy, Snoopy'ego, Snoopy'emu...
Charles, Charlesa, Charlesowi etc. - without the apostrophe.
It's a bit more complicated (e.g. there's no apostrophe in Charleya or Charliego because of phonetic reasons), but the general rule is that of two vowels vs. a vowel and a consonant.
Nevertheless, many people are confused about it and they put apostrophes whenever a foreign word is declined, like in your example. Still it's an error.
I'd say it's just termin. Termin ostateczny would be the ultimate deadline.
The translator applied the Polish miejscownik ending to the English word.
Nothing wrong with it. I mean, it's better to use a Polish word whenever an equivalent exists, , but if a foreign one is used, it should be declined, if possible. And deadline is very easy to decline, it would sound unnatural if left undeclined.
"Przed weekend'em muszę, zrobić pranie""Przed lunch'em spotykam się z Piotrem"
And these are examples of incorrect use. It should be "przed weekendem, przed lunchem". No apostrophes here.