(1) Does "to make a convert" mean "to make a convert of my own"? Or "to make a convert of somebody else"?
He meant that he never tried to convert someone to his faith, which means to make a convert of his own. The "of my own" part means that he's acknowledging that others did at least try to make converts of their own.
(2) Does "in four words 'be just and good' is that in which all our inquiries must end" mean "'be just and good" must be the ultimate goal of all our inquiries"?
Yes, after 50 or 60 years of reading about religion and philosophy, he sums it all up in just those 4 words. That is, all the religions and philosophies he's studied can be that easily summarized.