The title is clear, this post is to share experience with the community.
I will answer it myself.
As it turns out, after some searching, there is no EPCS128 but EPCS64 installed on the print.
The manuals of DE10-NANO & DE10-Standard both refer to EPCS128, replacing EPCS128 with EPCS64 fixes the problem.
Correction: DE10-Standard has effectively EPCS128 why but the remark about My nano remains valid: EPCS64 and not EPCS128.
Why the download of the DE10-Standard failed at 88 % is still unclear.
Yes issues were resolved:
for the DE10-nano: it is solved (configure EPCS128->EPCS64)
for the DE10-standard all of a sudden, download succeeded.
Thank you for asking.