How can I specify the values that get stored in the grid for a checkbox? For example, instead of "0" and "1", I want to have "T" and "F"?

You can specify with

    style.SetUserAttribute(GX_IDS_UA_CHECKBOX_CHECKED, _T("T");
    style.SetUserAttribute(GX_IDS_UA_CHECKBOX_UNCHECKED, _T("T");

that T and F should be used for checkbox state instead of 1/0.

Just apply these style settings to the column style e.g.

   SetStyleRange(CGXRange().SetCols(nCol), CGXStyle()
       .SetUserAttribute(GX_IDS_UA_CHECKBOX_CHECKED, _T("1");
       .SetUserAttribute(GX_IDS_UA_CHECKBOX_UNCHECKED, _T("0"));