When you write an article for distribution, how many different sites and/or directories do you usually submit it to?
About 6 - but only the top ones. Don't waste time on the small ones, in my opinion. Takes maybe 30 minutes per article, but I usually can expect at least 25 and maybe as many as a few hundred links out of it. I have a newer site that has no reciprocal links at all, but I wrote 4 articles about it and one of them got picked up from a top directory and was used in one of the industry's biggest email newsletters. The exposure of that one article now has that site ranking #1 on a major search engine for 2 keywords that get a decent number of searches. All of that from a grand total of about 3 hours of work (2½ to write the article and about 30 minutes to submit it).
If 5 - 10 sites have already posted one of your articles, do you keep on submitting it at more places or stop?
I stop. There's no real harm in continuing, but as long as you're hitting the top directories in the 5-10 you submit to, it comes down to using your time wisely. From my experience, the vast majority of these sites are just a waste of your time. Your time's better spent writing more and submitting to fewer sites that are the top dogs.
When you write the next article in a related group of topics, do you submit again to the places that published your articles previously, or focus more on getting links from different sites for the next round?
If you stick to the bigger, established directories, which get a ton of traffic daily and from a wide variety of sources, your exposure is huge compared to the little ones. You have no control over who will pick up your article to reprint it, so it makes more sense to go after the widest audience, even if it means some level of repeats. It's a good idea to find some sites on your own to submit your articles to, as well. Don't only submit to directories. Look for sites in your industry that are not direct competitors and ask if they'd like the article for content on their sites. Just require them to leave your link(s) in place. Those are some great one-way links!
Are there any drawbacks to submitting articles to article directory sites?
Can't do your site any harm, per se. You need a thick skin because some of those who you find using your articles will not give you credit or a link. Comes with the territory. It's not worth my time to pursue that or get into an email argument. I ignore it. The only drawback I can think of is that it does take up your time. But, since getting links is critical to ranking on the major search engines, it's a valid use of that time.
One other thing I try to keep in mind at all times with this subject. Don't just think of the search engine benefits. The more articles of genuinely high quality you write on your topic, the more credibility you build in your industry. You (and by extension, your site) will become known as an authority, and that can be like printing money. It takes time, but I've seen it pay off with at least one of my main sites in about 14 months. You'll notice that your site is getting traffic flowing in from non-search engine sources as the number of links grows. Keep plugging away with good articles and make sure that it isn't all wasted when people get to your site! Great content on your site is the ultimate means to your goal of making a living from it.