Can i Put electronic thermometer into the water to measure the temperatue? Will that make the thermometer broke?

I think most thermometers intended for kitchen use (with some part that sticks down into liquids, boiling sugars, or hot oils) are fine up to 212 F which is the boiling temperature of water.
So unless you want to achieve higher heats (with frying oils or melting sugar for candies, etc), most of those would give you at least a general range of the temperature of a liquid/etc you wanted to measure, or the inside of a meat (though you'd need a pointy thermometer for meats, etc).

Some thermometers will need to stay in the liquid/etc longer than others to register a correct reading though.
(And some thermometers can't go in the oven or in any other situation where the temperature around them will be higher than 400 F, but that's not what you asked.)

Check out these kitchen thermometers (with some kind of long part) to see which you have and what their temperature range is:
https://www.google.com/images?q=food+thermometers
https://www.google.com/images?q=candy+frying+thermometers
https://www.google.com/search?q=meat+thermometers

Then you'll know which ones might work for the food you have in mind.

If its a food thermometer, of course you can. thats what its for. Water, gravy, sauces, meats, etc. The probe part only, not the whole darn thing.