Expert Archer and Fighter Training are both untyped bonuses, they should stack.
I don't think there is any combination of levels that would let you go above the +4 bonus that normal fighters get from weapon training so it shouldn't be a problem really. In fact you have to take 4 more levels or archer or 6 more levels of Myrmidarch to get another bonus. So, if you took 8 more levels in archer you would be 19th level and have a +4 bonuns to bow attack and damage. If you take 6 more levels in Myrmidarch you wont be able to get any other bonuses at all and would end at +3.