1)I have made mung beans sprouts.
This is not quite right because it implies that you created in the sprouts in the the way you might say "I baked a cake." = "I made a cake." "To make" is not typically used for growing plants. As @Kace36 said in the comments, "grew" would be more appropriate. Grammar is fine in this one, but usage not quite.
EDIT: @Roger Sinasohn is correct. This is not exactly grammatically correct. This should be "I have made mung beans sprout." (sprout as a verb) or "I have made mung bean sprouts." (sprout as a noun).
2)I made mung beens to sprout.
So...spelling of "beans", obviously. Grammatically, infinitive is not use here. "I made mung beans sprout." would be grammatically correct, but still have usage issue above.
3)I kept mung beans in water, I got sprouts.
Grammar is fine here. Usage is a little odd. "I put mung beans in water, and they sprouted." would be more natural.