I will ask some questions to help you figure out some important details in your story.
A couple of questions about how the inmortality works in humans:
I know they can`t get sick or die of old age, but they can be killed or hurt?
If they are incapable of being hurt, how can someone take their blood?, do they have a weakness?
Alright, that explains how the inmortality can be transfered. But now i have another important question. How easy or hard is to spill inmortal blood?. If it is too easy, inmortality can be easily transfered.
Why having only one inmortal race keeps a balance on earth?.
This must be clear, so it doesn`t feel like a plot hole.
Here is an idea for the explanation:
The inmortal race is the dominating race in earth and the one in charge of keeping the balance and order.
Why she kept the humans and phoenix away from her brother`s creation?. Why she transfer the inmortal blood to humans?, did she went against her own creation the phoenix?, and why?
Don`t worry,this is your story, so you can make your own version of phoenix.
Hope this helps.