Translation:I hate going to the hospital.
"i hate going to hospital" was what I had too and it's still not allowed
It turns the verb phrase 病院に行く (go to the hospital) into a noun phrase (going to the hospital).
Both are grammatically correct. Among other details, the nuance here is that は emphasizes what comes after it: 嫌い. If が is used, it'd emphasize the subject/topic: 病院に行くの. は: "I hate going to the hospital." versus が: "Going to the hospital [is a thing] I hate."
So using の here after the plain form of a verb changes a verb into a noun, like gerunds in English? So in the sentence, 'I like running', 'running' becomes a noun. Likewise, 走るが好きです means 'I like to run', but 走るのが好きです means 'I like running'?
Sort of yes. の is used to create noun phrases. So "走るの" is something like "the act of running". But you have to use this if you want to say you like to run or that you like running. "走るが好き" is grammatically incorrect, it has to be "走るのが好き".
It's awkward. In US English we'd say "I hate going to the hospital".
Oddly, your sentence would be fine with "love"--"I love to go to the hospital" sounds just fine to me. I'm not sure exactly why.
"I love to swim" and "I love swimming" both sound good. "I hate swimming" sounds good, but "I hate to swim" sounds awkward. That's why English can be weird I guess.
I feel like dislike and hate hold very different weight. I think dislike would be more along the lines of saying 病院に行くのは好きじゃない
Why Is "wa" used instead of "ga" here? In the tips and notes section they only use "ga".
Why is there a の before は? As far as I know (の=belong to) so that doesn't make sense! !!