Ok, they have declined my gnupg sign, because it's not legal/official in Germany to use it. I will make a picture of my hand written signature and add it with Gimp (they even recommended me to edit the pdf and add a scan of my signature). I can't believe that this is a legal way, because the result might look like the worst try of a scammer.
You may be able to print a PDF, sign it, then fax it. I'm not sure if everyone will take a scanned signed document as proof, because that could so easily be faked by someone else.
I've printed a document, signed it, then scanned the whole thing, and sent it in the past. They accepted it then, but now after how more become adept at scams and thinking how that can be scammed, I see problems with that. Adding a signature with Gimp doesn't seem like the way to go. At least it should be signed in physical form, then scanned (,or photoed) and sent.
It may be little different than a faxed document. If they take signatures in faxes, use Kinkos, UPS or an office supply store. They scan, print and fax for you for little cost. And if you don't use a cover letter, some people are so stupid, they'll get it, but they'll throw it out, and say they didn't get it based on that it didn't have a cover letter.
If they accept Adobe PDF Reader, LibreOffice should be little different, but maybe they have digital ways to preserve the integrity. GNUPG sign doesn't look much different, except for commercial assurances or reputation of Adobe's product.
By fax or email, give power to somebody you trust to digitally sign the PDF in your place?
A notary can't sign in the place of the person, but they sign or stamp in addition to. I'm unsure if some have services to fax or digitally send it for the customer.