I think it's a fine idea to write to your favorite author, or anyone else. Don't do it if you'll be disappointed if you don't receive a response. Authors in a PR mode will answer. Authors not in a PR mode will not.
Not necessarily so. Some authors, believe it or not, are real people. And they may just pull your letter out of their mailbox and drop you a line thanking your for your thoughts and/or comments. It is, of course, far more likely if you have met them at a conference or some such and you can say, "It was such a pleasure to meet you and talk with you over lunch at... conference in... last month." (or whatever) Then, of course, the next time they are going to be in your neck of the woods, you can drop them a line and say, "I see where you are going to be in my neighbourhood in... You've been so kind to me, I'd like to invite you to a respite from the road. A home-cooked meal and we can crack open a 23 year old bottle of Glenlivet." (or whatever) Next thing you know, you've got a good friend on the inside of the business who has connections and can hook you up! Another reason why those conferences are important!
The only clarification that might be needed in my comments is assuming by "favorite writer" we're talking about someone who has a vast readership, a famous writer in other words. Famous writers get duffel bags full of fan mail. I suppose there's no harm in dreaming the writer will "pull your letter out of their mailbox and drop you a line thanking you for your thoughts and/or comments," but you'll probably have as much luck playing the lottery. Pulling the lucky letter out of the week's duffel bag wouldn't represent an author who is a real person (believe it or not, as far as I know every author we're talking about is a real person), it would represent an author operating a raffle. PR mode. I think your fantasy about dropping over for a home-cooked meal and fine liquor fairly proves my point. There's nothing wrong with dreaming, except when it interferes with your perception of reality. These people simply don't have time to respond in a personal, friendly, one-on-one manner, unless they're in PR mode.
Point well taken. Sorry. Didn't think I needed to underscore the sarcasm there. Not really a fantasy. But I won't make a grocery list of writers, actors, and politicians with whom I have broken bread. Which is actually what spawned my comment on "real people". You might, in fact, be amazed at how personable and genuinely warm and open and down-to-earth some of these demigods of the ink can be. Sure there are some total attitude pigs who buy into all of their own hype. Some are not. And some, as you gently pointed out, might not have reached that pinnacle and, therefore, have not adopted the ego that so often (but not always) accompanies those public accolades.