If you are the one doing this and this is your own site, I would use a Physician as itemtype then medicalspecialty then additionaltype (which you did right)

They will do whatever it is that they already do and their system handles the rest.

Emailing them might work. Sometimes it can change but dont get your hopes up. You can try, then follow up on it. It is yours after all.

If they dont, then be happy with a nofollow link.

Referrals wont hurt

It just means that you have those things on separate pages. Google indexed them so like Laura said, you need to put a noindex tag so Google can stop indexin those page

After that, wait for it to disappear. It's not that critical if you feel like you need to remove it from the index asap.

Itll always be the case. Youll hit a plateau eventually.

There will be some things you need to do, from A/B testing design tweaks (and extra features to push them to other pages)

or you can compile a list of keywords you are already ranking for but below #5 and work on those to move them to the top 3

or you can utilize other traffic channels such as social to push them to category pages so they can look at other news.

I would advice to put everything on one page. (This is also great for a broad keyword)

Then have short descriptions in there the a link to a specific page for each service. (Specific targeted keywords)