At a high enough resolution the enhancer histone marks will flank the the open region. This is generally visible in averaged metagene type analyses. However at low resolution you should see these marks at enhancers (H3K4me3 is more a promoter mark than an enhancer one, though you will see some at enhancers). However, I wouldn't go so far as to say that those marks are causative for open chromatin and you'll definately see open chromatin without them, and I guess you'll also see those marks without open chromatin.
As for which comes first.... I'm not sure anyone know? The mechanism by which enhancers become active is still and open research question. It is known to involve pioneer transcription factors, which act to open up the chromatin, but whether those factors recruit histone modifying enzymes, or the modified histones help with the recruitment of the pioneer facts, or both things are happening, I don't know.
Where ever there's a histone you won't have an ATAC peak, since it's not open by definition.