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Hi. In contexts like this " Would " combined with " like / love " is a polite way of saying  " very much want to ". Example: a- Do you want to go to party with me? b- Sure, I would love to.

Hi. It means nothing to my knowledge. It's  just bad English. " Making a big effort " would make sense.

Hi. For the same reason "s" is  added to the end of "know" in the same sentence. The verb "see" needs to agree with the third person singular subject  "Hamlet".    "Hamlet sees a person (him). Hamlet knows the truth".  Paraphrase:       As soon as Hamlet sees him, he finds  out (knows, realizes) the truth.