Can I save money in Germany with OHA, like I did with BAH?

No. Been a couple years and am unaware of any changes (still have a couple friends there complaining about this) but OHA pays your rent, up to your cap...not like BHA that just gives you all of it up front. On the bright side you will also make COLA. That you pocket and do with as you please. Big $ if you have a family.

Also, if you rent off base many places offer utilities included in the rent. More often than not it's just a couple things versus all utilities but there are some that do everything. As long as you stay under your cap that's good. If you pay out of pocket make sure you watch your bill's. They like to do averages each month based off past usage. If you over you pay you get the difference back at the end of the year. If you under pay you get an extra bill. Most of my subordinates got a shock at the end of their first year when the bill came. Heating oil always sucked to pay for and they learned quick not to leave lights on all the time. Those weren't fun bills if you didnt budget for them.

V/R
Bogie

OHA calculator:
https://www.defensetravel.dod.mil/site/ohaCalc.cfm
Unlike BAH, you have to find a rental first, then provide a signed lease and fill out paperwork to start OHA, see the FAQ list:
https://www.defensetravel.dod.mil/site/faqoha.cfm

You can’t live ‘on your own’ unless there is no availability. Most of the family housing is outside the gate in the communities, but the military takes care of all the bills/utilities. If you did get approved, do you speak/read enough German to sign a rental agreement? I recommend taking what you are offered for housing.