I'm by no means an expert in writing utensils of that period, but before you go without any reply at all, here's what I feel comfortable offering:

I've seen quite a number of various official 3rd Reich military documents and a bit of civil administration stuff (mostly marriage licenses, aryan certificates and such) over the years, and I cannot remember ever having seen any formal writing on them that didn't look like fountain pen ink, or exceptionally neat writing with dip pens. Dip pens have a tendency to distribute the ink more unevenly than a fountain pen and are prone to blotches - someone who doesn't write with them regularily will be easy to spot. On the other hand, 1930s/1940s German clerks in a stationary office, who do a lot of writing in ink on a daily basis, may very well be able to use a dip pen in a way that makes it nearly undistinguishable from a fountain pen to the casual observer. German school children of that age were trained in writing with dip pens and (according to contemporary witnesses from my family) were only allowed to "graduate" to fountain pens when they had sufficiently mastered proper writing technique with the dip pen. There even was a specific standard of nib (called Schulfeder) especially for schoolchildren which you still find on ebay/German antique markets from time to time.

As having open ink wells around would be rather unpractical in any military situation outside of a stationary office and newer model fountain pens were considerably less prone to leaking than those from before the turn of the century, most military personnell in the field (and definitely most military officers who may need a writing utensil at hand any time) would have used fountain pens. Popular German brands of that time were Sonnecken, Brause, Pelikan and Mont Blanc, the last already having a reputation for excellent quality and being a little more expensive than the others even back then, but by no means the pure luxury article it is considered today. if you browse the German ebay, looking for "Füller Antik" in combination with the company names, you'll find many good examples - the basic look (predominantly black, bakelite/plastic, pen-shape, rounded edges, no or few fancy trimmings) really hasn't changed very much until a lot later in time.

All informal corrspondence I've seen from that time period (letters and postcards) was in fountain pen ink, or in a few cases in pencil. Note that most of the pencil stuff was rather hard to read by now, so it is entirely possible that pencil writing might have been a lot more common back then than the number of artifacts remaining suggest to us now - the latter is wild speculation on my part, hopefully you'll also get an expert's reply who might shed some light on that, as I'd be curious to know as well. For what it's worth though (anecdotal evidence leading to speculation - mods, please do feel free to slay me for this): My family has retained a suitcase full of old personal documents from the last roughly 150 years, most of it formal and informal correspondence, among them many letters to and from soliders fighting in both world wars. What always stood out was the great care with which the "special" ones were written - birthday and holiday letters always used the "good" stationary, even when most anything else was already written on cheaper/thinner paper and the penmanship looked especially careful. I would therefore assume that any lady writing either to a deported child, or to any official on behalf of one, would use ink instead of pencil. As far as rolling pens/biros are concerned: To the best of my knowledge, they didn't see widespread use in Germany until at least the 1950s.

I hope this is of at least some help to you - best of luck with your play in any case!