I roughly anticipated all expenses to amount to roughly 4500 euro per month, that includes food, housing, travel, etc.
Well, depends on your lifestyle and the unit/area you're posted to..... Once again my 5 cent: 4500€ should fit in the northern part of Germany. In the south I'd add 1k. e.g.: I've a monthly rate of 2700€ just for housing in the southern part and I'd say you'll need additional 2500€-3000€ for a family of four for a decent lifestyle.
PS I too am hoping to move in August to start training in October.
Do you know, where you're posted to?