Wow, lot's of questions! Glad you liked the pictures and I'll try and answer as fully as possible.
Bill Skinner: As Curious_Aardvark said it's not in fact a rock but a 3 ounce bag of dried peas wrapped in duct tape, which looks surprisingly rock like from a distance but slings well and won't injure someone. In the second picture the Saxon line is indeed about to receive a Norman archery bombardment, with the slingers moving forward to skirmish the archers.
Alex.Ost: As I said they're not rocks but essentially duct tape beanbags. I didn't actually run out of shots in the battle (I bought 110 bullets onto the field and used about 80), however it did involve a lot of the slingers running forward to scavenge shots back when the armies broke up.
Parmenion: I've never larped with a sling, since I've never really found any systems that are friendly to it, but I'd be interested to hear if you know any? And yes, it is a sculpture of a giant arrow. Not sure why English heritage thought that was a good idea.
Curious_Aardvark: I was at Tamworth, and I took my original sling test there. We did meet, as I still have your business card, but I don't blame you for not remembering me
. Hastings was great fun, and we did get some good volleys onto the Norman line. The guy in the second picture is Taran, one of the Viking's best slingers and a sling thegn.