It is alright to use the same contraction, 'He's', to mean both 'He is' and 'He has'? Example, " He's angry.", "He's been angry.", He's a beautiful house."
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Yes and no.
You do use "he's" for "he is" and "he has".
You do use "he's got something" for "he has got something."
You do not use "he's something" for "he has something." [Note that according to @Optimal Cynic this is allowed in some parts of the world]
Therefore the first two sentences you proposed are correct:
But the third one is incorrect. You cannot shorten "he has a house" to "he's a house." You can only shorten "he has got a house" to "he's got a house." [Again, note what @Optimal Cynic claims]
Yes. He's can mean either he is or he has depending on context. She's and it's work the same way. Pick any reference.