Yes, you can go ahead and schedule the medical exam even though you are not yet married. I encourage you and your future spouse to set an appointment with an immigration lawyer to learn more about the process and timing involved in applying for your "green card". See the link to the American Immigration Lawyers Association below.
Yes you can. An issue that I see is whether or not your J is subject to 212(e). If it is, then you have to obtain the required waiver before you apply to adjust status and not concurrently.