What was the weight (preferably in grains) and speed (preferably
muzzle velocity in feet per second) of the projectile fired by the
German Model 1871 11mm service rifle using standard German military
service ammunition?

Hello chrisnp and thank you for your question.

German Model 1871 11mm service rifle:

Projectile Weight: 386-grain, roundnosed paper patched bullet.

Velocity: 1,443 feet per ssecond.

For further information see:
"The cartridges for the Model 71 and 71/84 rifles were very similar.
The 71 was loaded with a 386-grain, roundnosed paper patched bullet.
The charge was 77 grains of black powder, giving 1,443 fps velocity
from the long 33-inch barrel."
http://www.riflemagazine.com/magazine/article.cfm?magid=56&tocid=750

Thank you for your question, and if you need any clarification of my
answer, do not hesitate to ask before rating my answer.

Very best regards.

THX1138

Search strategy included:
1871 mauser feet per second
://www.google.com/search?hl=en&safe=off&as_qdr=all&q=1871+mauser+feet+per+second&spell=1

Perfect.  That's just what I was looking for - Chris