Your doctor is mostly right, and it sounds like he knows how to treat molluscum
contagiosum. However, he is wrong about transmission; in adults, the infection is almost entirely sexually acquired. As in your case, lesions occur mostly around but not on the genitals--lower abdomen, scrotum, and thighs are much more common sites than penis or labia.
On to your specific questions:
1) The virus may remain latent in some cases, but probably rare.