Can a guy touching your breasts cause breast cancer?

Not at all. Some breast cancer is related to heredity and runs in families. Most of the time, we don't know why it starts. But touching the breasts has nothing to do with it at all. In fact, breast self-examination is one of the best ways to find a lump, which should be checked by your doctor to see whether further follow-up (mammogram) is needed. Don't let anyone touch you there if you don't want him to.
No. Historically, breast cancer has been far more common in celibates than in sex workers / married ladies. Life's difficult enough, and good simple pleasures often criticized enough, without people scaring you like this.
No. No correlation. Biggest risks are genetics and, in a complicated sense, hormonal. Be safe in the rest of your love life!

Related Questions

Could a guy still get breast cancer?

Yes. Maybe 2000 men get breast cancer each year, almost always as a lump on the nipple. We're catching it earlier nowadays but still around 400 men die of it yearly. Read more...