I'm not familiar with the exact kind of heater you describe, but I actually just got a new heater yesterday, and so just recently got answers to many of the questions you're asking.
If the heater is a submersible, it can be fully dunked in the water, knob and all. Unless the packaging that came with the heater specifically said it has an auto-shut off feature (which will shut the heater off when water levels drop below the water line on the casing), do not assume it does! Always unplug it before doing water changes or taking it out of the water for any reason.
Now, as for recommendations for a new heater: The heater I bought is an All Glass brand submersible. I was really paranoid about getting a crappy heater and accidentally cooking my betta, so I wanted to make sure I got a good one.
I like the fact that this heater has precision temperature setting. That is to say, the little knob on the top has demarkations for degrees of temperature, which allow you to determine the exact temperature at which your water should be kept, as opposed to some other heaters which only raise the water temperature to a couple degrees above ambient (whatever the room temperature may be at the time). I've also seen other heaters that have knobs with just plus or minus signs, as in "crank thisaway to make it warmer, and crank thataway to make it not so warm!"-- I was wary of those, simply because I didn't like the guesswork that would be involved in trying to set the temperature properly.
I also like that this heater has the auto-shut off thingie, an indicator light to tell me when it's actually on, and a lifetime warranty (which would suggest to me that this particular kind of heater doesn't go on the fritz very often, and can thus be trusted). The All Glass heaters were also highly spoken of by other hobbyists. The only problem I have with it is that it says "ALL GLASS AQUARIUM" in big red letters on the side, and is really hard to miss seeing when looking in the tank. I should really stick a plant in front of it, or something. >_>
So there ya go. Those are some features you may want to look for in your new heater, if/when you decide to get one. The Visitherms that were mentioned earlier have all of the above features, I believe, with the exception of the indicator light, and are also very highly recommended by most (the warranty on them may also only be for a couple of years, but meh). The Visitherm Stealth model is particularly nice for tanks with black backgrounds, since they virtually disappear into the decor.
