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

I found some free hay bales today that were to be throw out so I grabbed
them 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 rainy
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