1. “The room strikes nice and warm on coming in” May be grammatically acceptable in casual speech, but I think “The room feels nice and warm when you come in.” Sounds more natural.
2. “When he arrived in Chicago, his friends met him at the station.” Your original sentence implies that this friend’s arrive, but I think you mean “when he arrived.”
3. I would say: “It seemed advisable to get an early start in order to reach the summit by noon.” Or “It was advised to get an early start to reach the summit by noon.” It also may be better to specify the who in the sentence. “We were advised to get an early start in order to get to the summit by noon.”
4. “By working hard, the task was finished.” One may read this sentence as “the task worked hard and finished. Work on clarifying who worked hard, name the subject: he, she, you, I…
5. “To make a long story short, the boat capsized.” This is fine I think.
I hope this was helpful!