I’m confused as to what adding こと to the end of… seemingly anything does. For example, the title of a recent Japanese Only thread is ヘリコプターに乗ったことはある. What is the difference between 乗ったことはある and 乗った? Are they interchangeable? If so, why use 乗ったことはある if you could just write 乗った? Is it more colloquial???
Another example I’ve seen is adding のこと to the end of nouns, like the thread titles 自分のことを誇りに思いますか?Would 自分を誇りに思いますか?have the same meaning?
こと turns a clause into a kind of noun phrase, and ことがある (and here thus ことはある) talks about having had an experience. In the first example you gave, it’s being asked whether people have had the experience of having gotten on a helicopter.
ヘリコプターに乗った?
Did you get on a helicopter? (Plain past tense)
ヘリコプターに乗ったことはある?
Have you been on a helicopter? (Emphasising it as a new topic, and talking experientially - we might say ‘have you ever been on a helicopter?’)
ヘリコプターに乗ったこと
The act of having ridden a helicopter
ヘリコプターに乗る
To take a helicopter, get on a helicopter (present tense)
You might want to look up a more in-depth explanation of ことがある and nominalisation if こと is giving you broader trouble.
Your second thing is a different sense of こと, the noun meaning matter/thing/circumstance/etc.
Already answered, but anyway. こと (and の) can turn a verb into a noun. Because of the grammar, a verb can only be a modifier for a noun. In you example you are modifying a verb (ある) using a particle (は), which requires a noun.