First of all, you've given a quote- from a book in French. Does the quote refer to English life in Jane Austen's times or is it a generality that spans several continents and centuries? How does it apply to Mr and Mrs Collins?

If you want to answer the question "Does, or does not Mr Collins spend much time at home?" You've first got to define "much time". Surely the first place to look is P&P itself, and to work out how much time is spent in the house, in the garden, in Mr Collin's fields with all those trees that he makes Lizzy count. How much of that time is "at home", by your definition? How many church services can you count in the book? How much of this time is spent where he could be "forgotten"?

Or are you actually asking to know what a rector actually did for a living? It would take a book to describe that- in fact it has taken several books. The best one I know of is Jane Austen and the Clergy by Irene Collins. That'll also tell you what he parson's wife did, and his servants and children. Probably the next best would be the personal diaries of some of the contemporary parsons. I happen to like Parson Woodforde's, but there are others. You might also like to look in the archives to find what's been said already, because a great deal has already been said.... ;-)

Was there only one sermon a week?!?

Wasn't JA's father also teaching boys at his home?

Those questions are actually answerable in short conversational format! The answer to the first question is.... Yes, sometimes. The answer to the second question is ...Yes, sometimes.