I would choose the human in both situations.

Lots of animals die due to our existence and not just for our food. We accidentally kill things all the time with our vehicles and the pollution we cause. I wish it wasn't the case but you can't step outside without ruining some ants day.

To then be faced with a choice between killing one more animal or a human... my heart would bleed for the monkey but to do anything else would be murder and pretty hypocritical unless one lives an extremely vegan and eco friendly lifestyle.

No medical issue will strip away the fact that it is a human life. I'll make it more absurd for you... they could have a terminal disease and likely be dead tomorrow and I'd still choose to sacrifice the monkey to give them 24 more hours.

Wouldn't sacrifice any humans for a billion monkeys

If you were a monkey, would you sacrifice a billion humans to save a monkey?

Or equivalently, would you sacrifice a billion humans to save a robot that's twice as sentient as the average human?

I cannot really say what I would do if I was a monkey, it's like asking me what a circle with corners would look like. Too far outside my ability to imagine. I wouldn't sacrifice any number of humans to save any kind of robot either, unless it was a robot critical to human survival like a surgical robot in the middle of a natural disaster.

Would you save a monkey whose body contains antibodies for the cure for cancer for humans (or AIDS/HIV/whatever), or 1 human?

The monkey. The answer would be the same for just a vial of the antibodies, the monkey is completely incidental.

coma: monkey

brain damage: now there's a hard one