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

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.
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.