if they are restrictions you could add them as cost, use type: restriction, restriction usage: prohibited
name it and press ok,
the new cost has added to attribute tab, double click on it, on the source value tab, change type to field, choose depth field for value,
now click on evaluator properties,
as you can see the Value = [Depth], change it to Value = [Depth] < 4000
do it for both edges [ from to - to from]
works fine here
for the second problem,
on the network analyst toolbar, click on network analyst window, click on route properties, from the analysis setting tab, select facility to incident