A. Do you fancy coming on a day trip to Perth next Sunday?

• The correct form is "coming" after the verb "fancy."

Nick spends the large hours watching everyday although he is trying to improve his communication skills.

• "The large hours" is not an idiomatic expression. We should use "many hours" or "a lot of time."

I don't intend to have to get up when it's dark outside.

• The phrase "to have to" is redundant here. We can simply say "I don't intend to get up."

For some people, training puts to my hand work.

• The correct preposition is "at" in this context. "To put one's hand to work" means to start working on something.

There are some times when everyone seems to be reluctant.

• The verb "seem" is already in the present continuous tense, so we don't need to use "to be" before the adjective "reluctant."