We always say that sheep don't read the books...
When he gets up does he stretch? If so, he's a contented lamb.
It's an encouraging sign, yes, but it's not absolute. I have had undernourished lambs that stretched when they stood up - but who were not getting enough milk to keep a fly alive.
A wagging tail is a good indication he is latched on and getting milk.
Absolutely not. Their tails wag when their minds are on milk, but it is not any kind of an indication that they're latched on and actually feeding. I have seen no end of lambs wagging their tails while they suck on wool, while they're seeking the teat (but not yet found it), even when nibbling my trousers

Again, it's an encouraging sign, but don't rely on it.