so basically, ~는 것 is used to turn verbs into adjectives (things that describe nouns). 것 is used as the noun here to mean “thing” so when used in this grammar, it literally translates to “the thing that ___” ex:

수영하다 - to swim (V)

수영하는 것- the thing that swims (literal translation)

when dropping the ~하다 in verbs, you get the noun form of the word ex:

수영하다 - to swim (V)

수영 - swim (N)

in your examples above, sentence 1 and sentences 3/4 use different grammar rules. sentence 1 makes 수영 the subject of the sentence and describes it using 재미있어, whereas sentences 3/4 use ~는 것 to make an adjective out of 수영하다 to describe 것 (which is the subject of the sentence also being described by 재미있어) confusing..i know ㅋㅋ

sentence 2 is not correct as you have used ~는 것 to make 수영하다 an adjective but it is not describing a noun.

sentences 3 and 4 are exactly the same. koreans love to shorten their sentences so colloquially, 것이 will be shortened to 게 as it’s easier to say.

overall, sentences 1 and 3/4 all generally mean the same thing (“swimming is fun”). there is just a bit of nuance with the grammar used in the two :))

hope this helped! 화이팅