Is it appropriate to send the abstract to the editor and ask him if my paper is a good fit with the journal? There is a very good journal in my area, but I have never submitted any paper there. Now I have a new study, which I think might be a fit with the journal but I'm not sure. So I want to send the abstract to the editor and ask him whether it's a good fit. If he thinks it's not, I wouldn't waste my time submitting it there. But is it appropriate to ask the editor to do this? What would an editor usually do if he/she receives such a request?
Sure.  The benefit is really not to get wrapped up with a long review cycle for something that doesn't make it in anyways when you could have gone elsewhere.  

That said, I think the very top journals (in science at least) like Science, Nature, PRL are pretty up front about weeding out stuff that is not notable and also committed to some speed in publishing.  So you might just get a fast answer on notability, regardless by running through the regular submissions process.  "We just don't publish cuprates that don't superconduct" was an actual editor communication from one of those magazines.