To answer your first question,
"If the situation asks for it, should a mountaineer be donating blood at higher altitude?" I'm assuming you're referring to a life and death situation on the mountain where someone desperately needs an emergency transfusion to survive an accident, and whether or not it is safe to offer your blood. My answer would be yes, you could, but don't expect to be making your summit attempt right after. Giving your blood won't necessarily put your body at risk of altitude sickness, but it will likely delay or postpone the rest of your expedition.
Acclimatization to elevation involves building your red blood cell count so that you can more effectively transfer oxygen from you lungs to the rest of your body.
After you donate blood, your plasma will replenish after 24 hours, but you're typically expected to wait at least 6 weeks to rebuild your red blood cell count. This process could take longer at altitude depending on the person:
The length of full hematological adaptation can be approximated by
multiplying the altitude in kilometers by 11.4 days. For example, to
adapt to 4,000 metres (13,000 ft) of altitude would require 45.6 days.1
After you acclimatize and donate blood, you won't have to repeat your acclimatization programme, because your red cell production will still be up from your previous programme. You will however be required to wait for your body to replenish it's red cell count from the blood you've lost.
I imagine that you'll feel somewhat the same donating blood at altitude after you've fully acclimatized as you would donating back home. If you already know how your body performs after donating blood, then you can probably expect it to perform the same at altitude as long as you're acclimatized and feeling fit. If you've never donated before, then I would NOT recommend trying it for the first time high up on a mountain, unless it means saving a life of a friend.
1 Zubieta-Calleja, G. R.; Paulev, P-E.; Zubieta-Calleja, L.; Zubieta-Castillo, G. (2007). "Altitude adaptation through hematocrit change". Journal of Physiology and Pharmacology: an Official Journal of the Polish Physiological Society