Does having a missing limb affect blood pressure? Wouldn't the heart still be pumping the extra pressure required for that distance?

No. If the limb were an upper limb it would just mean you would always have to take the blood pressure in the existing limb. Also if comparisons between sides needed to be done, the pressures would have to be taken in the thighs.
No and No. If the heart were a mechanical pump and our arteries were lead pipes, you would be right. High blood pressure is far more complex. The precise cause is actually not known, even in 2012! contributing mechanisms include regulatory function & hormones from the kidneys, central nervous system factors and others. Heart rate and force of contraction change as needed. Arteries dilate & contract.