Translation:The guy cooked for his new girlfriend.
en ny flickvän
sin nya flickvän
den nya flickvännen
ett nytt hus
sitt nya hus
det nya huset
The plural form of the adjective (here nya) is used with possessive pronouns (here sin) and with the definite form of the noun (here den nya ...en)
Can't you say får sin nya flickvän? I read somewhere there is a word for when you do something to help something rather than just doing it for them plain and simple.
You probably mean för, but that doesn't work. för is most typically used to denote an audience of some kind. Jag visade boken för henne 'I showed her the book', Jag berättade för honom 'I told him'.
When you do something for someone, you can use till – the normal preposition for recipients, or åt – often used to denote 'doing something so that someone else doesn't have to' (but it can also mean more or less the same as till, this varies a bit with different verbs).
In this sentence " The Lad" is accepted (and in fact suggested if you get it wrong) as a translation for "Killen". In the other sentence (Killen lagade mat till sin pojkvän), "Lad" is not accepted, only "guy" is accepted.
I have also learned "fästmö" for girlfriend. Which word between flickvän and fästmö is more commonly used?
fästmö is 'fiancée'. Flickvän is much more common and we don't use the other one unless she's actually a fiancée. Just tjej is very common too (for 'girlfriend' [in the romantic sense, not just a friend]).
Maybe I'm kind of late with this question, but if "lagar mat" means "cooking (food)", does "lagar" have a different meaning on its own, or is it still only used for cooking?