First, you should determine if your garage structure can support storage at all. The length of those 2x6 that are 11 inches apart (odd spacing, if accurate) will matter quite a bit in that. Or the drawings for your garage when it was built will actually tell you explicitly. 12 inches on center would have space between the joist faces of 10.5 inches, which would be "around 11" but also a more normal joist spacing...
For 1, normally whatever the stock size plywood sheet in your part of the world is - 4 feet by 8 feet is normal where I am. Sometimes for attic projects they need to be cut smaller to get them into place.
As for 2, you'll regret that when one slides off the joist and you step on it, it tips, and you fall either until you hang up on the joists yourself, or all the way to the floor below.