Pretty much what the title says
Am i allowed to make conversions to make miniatures into different poses or new details?
For example give a warrior with a spear a banner?

If so are you aloud to give a miniature a weapon thats not on its list?
like give an easterling warrior a spear.
Or an archer a crossbow

Lastly can you make infantry models into cav?

If the model represents well what it is supposed to yes. Conversions are indeed encouraged.
Doesn't really matter how you convert it as long as your opponent knows what it's meant to be.
To clarify giving a warrior who's meant to be equipped with bow an a xbow is not cool, However if a model has a hand weapon you could give it a different hand weapon for instance.
Try to aim for 'what you see is what you get' (wsiwyg)when possible.

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http://grungehog.blogspot.co.uk/

It also depends in which league you play. Some are more strict than others. Also the game you are playing (point match versus battle companies).

My understanding was that you can't give a model any weapon that is not listed as an option for that model - i.e, you can't give Galadriel a crossbow, you can't give Gondor rangers a shield. you can't give axes to elves or woses warriors, etc...

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T'was in the darkest depths of Mordor, I met a girl so fair..
But Gollum, and the evil one crept up and slipped away with her..

That's correct although the no axes to woses and elves is purely thematic

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http://grungehog.blogspot.co.uk/

A little late on replying again but thanks for the replies!