It Depends on the situation, but 좋다 is very often colloquially used to mean 'I like it'. However you generally can't use it if its something somebody else likes, in the third person you must use 좋아하다. I'm not certain about it's use in a gerund but I tend to assume any 1st person use of the word 좋다 at the end of a sentence can be 'I like'
They are all used to make the gerund/nominalization phrase.
것 is often contracted to 거 in casual speech. You can attach various markers depending on the sentence you are trying to make. The choice of appropriate marker is a question about nuance between topic/subject/object markers. But here are the various forms:
- 것 ↔ 거, no marker
- 것이 ↔ 게, subject marker
- 것을 ↔ 걸, object marker
- 것은 ↔ 건, topic marker