I'm making my first wedding cake for a friend. I will be using crusting buttercream due to the hot weather. The cake will have the rustic look where drag your spatula. I'm attaching a picture of how the bride wants the cake to look. Would this work with crusting buttercream?

Secondly, now if I decorate each layer, how do I stack the three tears without disturbing the decoration? Or do I stack first then decorate?

Also can I crumb coat , leave it to crust then add more buttercream to create the pattern desired?

I don't see why it wouldn't work, you would just want to add the detail to the buttercream before it crusts.  And yes, I would crumb coat, let it set, and then do the final coat/detail.  You definitely do not want any crumbs to show in the final layer.

As for stacking, I would keep extra buttercream handy in a piping bag, then once stacked, pipe around the base of the tiers to cover up the seams and do a quick swipe with your spatula to add in the detail.

I'm dong that exact cake in September!  Coming out of retirement for a friend.  Above instructions are the way I'm doing it.  Of course still stacking with SPS.

Would this work with crusting buttercream?...........Yes it will work just fine as you create the pattern before the icing crusts.

if I decorate each layer, how do I stack the three tears without disturbing the decoration? Or do I stack first then decorate?.............You stack then decorate.

Also can I crumb coat , leave it to crust then add more buttercream to create the pattern desired? .................certainly :)  As long as the top layer (of icing) is thick enough.