Can you get malaria from blood of infected person?

Yes. Yes. Although rare in the US, it is quite common in some other parts of the world.
Yes. You can get malaria from blood transfusion if the donor blood is infected with malaria. Coming in contact with small amount of infected blood with intact skin will not give you malaria.

Related Questions

If you get malaria infected blood on your wounded finger can you become infected?

Possibly. This is not likely, but certainly conceivable. The plasmodium is present in red blood cells and some forms free in the blood. Transmission through blood transfusion is well documented, and therefore blood into open wounds may due the same, but significantly less likely. Read more...
Extremely unlikely. Malaria has a complex life cycle: the parasite goes through one evolution in the mosquito which then injects the next form into you while biting. This form is quickly taken up by the liver for another evolution to turn into the form which infects your red blood cells. Another form becomes ready for the next mosquito. It is almost impossible to be directly infected by a small blood exposure. Read more...