How flexible and understanding are agents and editors about conflicts with an author's day job?
Mine have been very understanding and flexible. Most writers, especially debut authors, have day jobs, so agents and editors know you have things to do besides write all day. They do, however, expect you to be as professional about your writing career as you are about your day job. It's not a hobby anymore, and you have responsibilities to both your "bosses." But life happens and they get that, and they'll work with you best they can.
Do they assume that you will drop everything around the time of a book release to focus on signings and appearances, etc?
Mine haven't. They do expect you to do everything you can to help promote your book and get back to them when they have deadlines to meet, though (which are usually on your behalf anyway). You chose to publish, so you have your share of things to do to help promote your book. You can choose to do nothing of course, but then the odds of there being a book two go down, since fewer people hear about your book and read it. But remember, as a debut author, you won't have a ton of events to go to. They're also usually nights and weekends, and you're the one who picks the times and dates that work for you. On my signings I had several time and date options and I chose what worked for me.
Unless you're incredibly lucky, it takes a while before an author becomes a big enough name to do the tours and whatnot. You'll most likely start small and have a few local appearances, maybe a few festivals or conferences. If you get to the "on tour" level, it's your call whether or not you want to do it. Perhaps you'll be more comfortable doing things that work with your day job schedule, like online tours or radio bits. Or by then your day job boss will be more flexible to you taking time off for a short period to do events. There are perks to being famous ya know -grin-
At what point do you have the conversation with an agent about whether or not to quit the day job and write full-time?
You can always ask your agent day one if you wanted to. They're there to answer these kinds of questions. But I've read/heard that the average is five books or five years. If you're still selling, and are living off the royalties from your backlist (where it stays in print and keeps selling), then you can start thinking about quitting. But not every book makes it to backlist status, so the advance may be all you get. Since you can't count on selling a new book for X dollars every X months, it's too risky to quit.
And what if you don't want to quit the day job?
Then don't. If you can do both, do both. Lots do. Writing is one of those things you can do in your spare time.
Publishing is a business, so naturally there are things your agent and publisher will expect you to do. All jobs are like that no matter what they are. Luckily, writing has lots of flexibility, so it's a perfect side career if that's how you want to go.
On the flip side, it's not something you can start and then ignore if you want to build a career. Although I'm sure there are writers who toss out a book every five or ten years, most aren't going to be in that position. Debut authors don't have the name recognition to draw readers to them, so they need something else to tell reader their book is out there and to go read it. But there are a lot of ways to do that that will fit into all kinds of schedules.