Could I put some Galadhrim Knights and Haldirs Elves and stick to my theme of the Battle of TLA?

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"When Alexander saw the breadth of his domain, he wept for there were no more worlds to conquer."

No. It would look very out of place. You could convert some high elves as cavalry and use the Galadhrim knights' rules.

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"War does not determine who is right, only who is left."
- Bertrand Russel

Elves from Lothlorien would definately have fought in some of the wars of the Last Alliance, so thematically a list combining some Galadhrim cavalry with either High Elves or Men of Numenor would be ok imho. Adds some variation and character too, so I'd go for it.

Was Haldir alive during TLA?

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"When Alexander saw the breadth of his domain, he wept for there were no more worlds to conquer."

I'm not sure, it's unlikely but not impossible, I don't think he occurs anywhere in the narrative apart from when the fellowship are in Lothlorien but including his Elves would be ok, as they're just the warriors of Lothlorien.

I think it's entirely possible, and perhaps probable, that Haldir fought a the Battle of the Last Alliance. After all, he's an Elf and thus immortal. He could have even fought in the First Age.

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"There are few left in Middle Earth like Aragorn, son of Arathorn." - Gandalf, Many Meetings

Maybe Haldir was alive then but the Galadhrim were little concerned about the events that happened outside Lothlorien as their destiny was to go to the grey Havens anyway. I think Gil-galad went to the last alliance as he had already made a strong relationship (not that way!) with Elendil and thus felt obliged to join him at the black gate.

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"War does not determine who is right, only who is left."
- Bertrand Russel

Per my readings, when the Alliance led by Gil-galad passed over the Anduin they were joined by silvan elves out of Lorinand and Greenwood, led by Amdir and Oropher respectively. P 258, Unfinished Tales. The silvan would not submit themselves to Gil-galad's authority however, and Amdir and his forces were driven into the dead marshes, and Oropher did an ill-considered attack on Mordor that was highly unsuccessful.

As a result, fielding either Galadrhim or simple wood elves are completely in theme with the second age.

True, Unfinished Tales is a treasure on background information.