For (1), the more usual word order would be "Having seen her amazing personality, he gave her the job". (2) doesn't quite work.
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JumanahWhat about this?!~She'll go there tomorrow wanting to see him.Yes, that's possible.
JumanahIs it correct to say "she'll go there being excited about that"?It's not natural English.
JumanahBeing told about that now, her mother is angry.Is it correct?And is it okay to say "She being told about that now, her mother is angry."?!I suppose the second is worse than the first, but neither seems like natural English.
JumanahDo you mean the first and second sentences are grammatically incorrect?When you use the pattern "Being X, Y", the first part normally describes a state, for example "Being ambitious, she applied to one of the top universities". "told about that now" does not describe a state, so your example does not work very well, albeit it may not be strictly gramma