Is my paternal uncle entitled to demand $14,000 in exchange for registering my name with him at the Ministry of Housing, or am I obligated to pay $5,000 according to the initial agreement made before the pressure and threats?

We do not know whether you are entitled to the scholarship, but your uncle's demand for the money is not permissible for him, and you are not required to pay unless it is absolutely necessary and you are entitled to the scholarship, in which case your uncle would be committing a sin. However, if you obtained the scholarship through cheating and forgery, then the entire matter is invalid, and you are not entitled to the scholarship, nor is your uncle entitled to the money.