As a guy, is it safe to have an MRI if you and your wife are trying to get pregnant? The MRI would be on my shoulder, if that makes a difference.

Yes. Mri does not use ionizing radiation of any kind and is safe for both males and females re:fertility concerns.
Yes, it is safe. Mri's do not use radiation and have no known adverse effect on fertility.
Most likely. To the best of our knowledge, there is no side effect. The issue is much more sensitive in an actual pregnant female. But even in those cases, as far as anyone knows, there are no serious side effects. Of course, the science has only been around for so long so who knows what correlation might pop up after 20 years of followup.
Yes. An MRI study is completely safe for you.