1. The top horizontal trend line should have prices that approach and withdraw at least twice (in other words, two distinct minor highs). Similarly, two distinct minor lows support the up-sloping trend line. There is no mention of 3rd touch.
2. Prices need not touch the trend line but should come reasonably close.
3. The line need not be completely horizontal but usually is.
Your point of higher 2nd leg can be tacked: either by drawing the line little up or drawing it slightly tilted. However it is also mentioned in the book about a premature breakout which gives a hint of the forthcoming action.
I appreciate your comments that gave me chance to refresh my information on this pattern.
Here is the pattern : http://thepatternsite.com/at.html