They have a different implication. "I have already found it" is the answer to someone saying "I'm going to look for your bike," or something like that--basically a statement that implies that they or you should look for something that you know has already been found. Or, you might say this if you have found something surprisingly quickly, as in "Oh look, I've already found it." "I have found it" is what you say when you have found something in an unsurprising amount of time, or if someone asks you, "have you found it?"

"I've (already) found it." no difference

If to say "I have something" fast enough the sound "h" usually becomes dropped for the sake of speed and you'll get "I've something". But "I've" is a grammatically legalised contraction. (Not as "I gonna" instead of "I'm going"). But in some accents people do not pronounce the sound "h" completely, like "Urry, ave you eard tha' orse running?" (note that the mark " ' " is the dropped out sound "t" also for the sake of speed).