And thus "mercurous halide" is Hg_2X_2; and "mercuric halide" is HgX_2. As is common with "ous" versus "ic" endings, the "ic" denotes the higher oxidation state.
In HgX_2 the metal displays a formal +II oxidation state; in Hg_2X_2 the metal displays a formal +I oxidation state. Where there is an "element-element bond", as here in Hg-Hg, or in a C-C linkage, the 2 electrons of the bond are assumed to be distributed EQUALLY to the bound atoms. When we assign oxidation states for "element-heteroelement bonds", the most electronegative atom gets the 2 electrons from the bond.
And thus for HO-CR_3, we get formally HO^(-) and ""^(+)CR_3. The ipso carbon in ""^(+)CR_3 has a FORMAL C(+I) oxidation state.
I write "formal" guardedly. Of course with such designations, the assignment of oxidation number is very much a formalism, a practice with little fundamental significance, but there is utility in assigning oxidation numbers for balancing redox reactions.