I saw her before. I saw her already. Already means "by now" and before places the event on a time line. for example "I saw her before lunch" makes sense. "I saw her already lunch" does not make sense. Before is a preposition and already is not. Prepositions express relations to time or space. In this case time. Already is an adverb. Just like your example I have already seen her. I have seen her before. You can often use them to mean similar things but the sentence must be written differently. Before can mean already but already can not mean before. Hopefully that makes sense.

"I already see her" is incorrect. The correct form of this is the first sentence you wrote "I have already seen her" In your last sentence, I think you misspelled "saw" as "sow" in which case "I saw her before" is correct The difference in meaning is that already implies something recent and something that doesn't require seeing the person again while before implies at some time in the past and possibly with some confusion as to where. So: I already saw her/I have already seen her I went to her and don't need to go back to her to do what you are saying I need to do while I have seen her before/I saw her before I have seen her somewhere. Where was it? OR simply "I have went to her before"

I saw her before I met my wife.