Hi Micha,
many many thanks for this translation.
I've asked the "Armed Forces" experts if they can help us with some of the phrasing and technical terms

Here are a few comments from me, and we can gradually put a picture together.
I would interpret "Schwimmen mit Gezeug" as Swimming in full uniform"
Second thoughts: Maybe "swimming in full kit" would be more correct here.
Micha informed me that he has translated "Abteilung" as "Detachment"
I am wondering what would be correct here: Regiment, Company, Division, Troop ?? ??
(Had) to form up with his duffle bag for 2 days because of carelessness with his clothing
.
and a similar on later. I am guessing that there were set times for laundry and he didn't turn up on time.
Detachment order from. = Company order from
casern = Barracks
I. A. D. A. [Probably: By order of the admirality]
I agree: I.A. = Im Auftrag, a standard phrase meaning "On behalf of" , possibly like 'pp' in english ??
2 penalty-guards because he has not avoided that unauthorized (persons) entered the casern
2 Strafwachen ... I guess penalty watches. Could someone be given extra watch duties as a penalty ??
casern is Kaserne = (probably) Barracks
3 days middle-arrest because of noncompliance to a through/by ....
possibly "failure to carry out an order from ..."
Not doing his laundry on time, spying on the bathing beautys, disobeying orders ....
Lambendsor, It looks like your relative was a bit of a naughty boy

Bob