High HDL related to high cholester?

Yes. Total cholesterol measures the cholesterol contained in all lipoproteins including low density lipoprotein (ldl), intermediate density lipoprotein (idl), high density lipoprotein (hdl), very low density lipoprotein (vldl), and chylomicrons. If high hdl-c is present, total cholesterol will be increased.
High HDL. Is a good thing, that is the good cholesterol. Usually when people have high cholesterol, it is the ldl's that unfortunately are high.