"I went on a date with my boyfriend on the weekend."
kare can either mean he or boyfriend (very context sensitive). kareshi is (mostly) explicitly boyfriend.
(A person talking to you and gesturing at the man besides you)あなたのかれですか。Is that your boyfriend? (のかれ made it more obvious that it's meant as boyfriend, like (あなた/わたし)のかのじょ for your/my girlfriend.
The "shimashita" form of "suru" is the verb here. The verb "suru" usually turns a noun into an action and is preceeded by an article like (wo) or (ni) in some other cases.
Making a compound of a foreign word (kiss, date, knock, etc) with a form of "suru" is rather common in contemporary Japanese.
The verb can be a bit complex in some cases and it's used quite a lot, so it's worth reading a more detailed explanation.
デートする is the verb. There are many nouns that together with する form a verb. ( e.g. 勉強する)
I think the verb is 'デートする' or 'デートします'.
'旅行'(noun), '旅行する'(verb). like this. sorry, I can not explain grammar well.
this site seriously needs a comprehensive policy regarding the use of kanji. either use the damn things or don't, but don't change the rules between sections. Having been using 行く for go, for like the past ten levels, I don't expect to suddenly get told that it's wrong and I should be using いく. If they're trying to force me to use しました with the デート then don't give me a potential answer using いきました!!!!