Chain shirts are called a byrnie, then a haubergeon, then a hauberk. The nomenclature is rather confusing, but it seems to depend on how long the sleeves and torso are. Hauberks generally reach down to the knees for example.
Aluminum is more than strong enough for larping if all you guys use is foam swords. The rings will only come apart under constant strain and they will only break if you apply a spike of stress the material can't spring back from. So a real sword or getting your coat stuck in some industrial machinery would do the trick. Otherwise the only real problem you will have is the rings discolouring over time. But they will do this anyway because the rings rub together. A headpiece made of chain is generally called a coif.
Since slashing damage is the least of your worries agianst foam swords, a looser weave with bigger and thicker rings is your best bet. For serious armour you would instead want a very tight weave a with small rings.
In either case I would heartily suggest you get an arming coat. An authentic one is annoying to make, so you can just get a skintight t-shirt and add some padding under the armpits and on top of the shoulders. Makes weaking the mail a lot more comfortable.
If you haven't already I would suggest visiting the Maille Artisans International League webpage. MAIL get it? Its a rather large resource on all aspects of mail making. There are others, but MAIL is the best general resource I could find.