If I were to purchase a 16 to 18 foot dinghy with center board, how do they heel over before capsize?
It's a rather rubbish answer, but it really does depend on the boat. In older-style boats it is certainly possible to have plenty of water flooding over the leeward side-deck and still be able to save it if the sheets are free and you and the crew are still hiked out.
Are they able to sail on days with high winds of 20 mph or so without capsizing?
Yes, but it depends primarily on the skill of the sailor, the boat and whether you're able to reef. For skilled sailors 17kts (as a base figure) would be great racing conditions, although they would probably regard a swim as a possibility. For a beginner, I would say no unless you have the option to reduce sail area.
I would love to get a smaller boat to practice on as it is easy to set up and easy to find a place to sail it by myself.
Bear in mind the following:
In a dingy, you're the ballast and provide the righting moment.
Practically, this means that if you're short-handing a dinghy you're depriving it of a significant proportion of the righting moment it is designed to have. Depending upon the boat, it could make it very hard to beat in anything over 7kts (maybe 10kts) as you won't have the righting force to bring the mainsail very far on.
I would probably suggest starting out in F3 winds or less if you're learning to short-hand a dinghy unless you have the option of reefing. And, at least at first, ensure you have sufficient safety gear to cope with the possibility that you might capsize and, once righted, be unable to keep her up (a swamped boat is much harder to keep upright than a dry one).
Having said all that, my perspective on this is of someone who races dinghies where the designs don't really accommodate the level of flexibility you need. It might be rather different in dinghies designed for cruising.