Hay, a few questions for those who use hay as a mulch in their gardens.

I found some free hay bales today that was to be throw out so I grabbed it
to use as mulch when the growing season comes around. The bales are standard
pasture hay, grasses and whatever else was growing at the time of cutting. I
have no idea how old they are, no one could tell me. A couple of the bales
are actually growing grass on the top and all the bales are starting to go
mouldy inside. It is late late autumn here, the cold rainey season is upon
us..

A few questions for those in the know.
What is the best method of storing hay in this condition? I though either in
the (cool dry) garage or outside under a tarpaulin.
Do I need to worry about the mould inside the hay? I have heard the odd
story of hay self combusting when it rots, any chance here you think.
I thought to kill the grass simply by placing it face down and letting the
lack of light deal to it.
Anything else I should be aware of?

Thanks
Rob