How to do a promo for FREE book in German?

As Lyonesse said, pretty much everything written is in high German with some lexical variations between Austria, Switzerland and different parts of Germany. Some regional niche literature is written in dialect, e.g. there is a niche for fiction (and sometimes non-fiction) written in Lower German (which is actually a separate language rather than a dialect) in North Germany. But since you want to appeal to as wide an audience as possible, high German is the way to go, since that's the "standard" everybody learns in school.

Another exception is that for books set in Germany (or Austria or Switzerland), it's okay to sparingly use the respective regional dialect in dialogues and scenes from the POV of a German character. However, that won't apply to 99 percent of translated fiction.

The whole "new versus old spelling" debate is annoying, but it's not that big a deal and the old spelling continues to be used and acceptable. For a children's book, I'd go with new spelling, simply because that's what they learn at school.