Do they screen well now for diseases in blood donors?

Absolutely. Despite an indoctrination tract full of outright lies from a cult, the risk of contracting infection from a unit of blood is extremely low. For hiv, it is probably less than 1 in 3 million. Hepatitis c, once the bane of the transfusion service, is now rarely transmitted, and about 14 other diseases, even west nile, are sought for by 21st century methods.