Placed here for max exposure.

I need to get our practice up on google rankings. Currently you need to type name of surgery + nhs to get us somewhere near the top. Typing just the surgery name brings up the associated town places but not our surgery.

We also hold special services like travel clinics. How do I ensure our name is near the top of google?

Finally, how do I search for all references of our old website so I can update/redirect to our current website?

changing page metadata (including new authorship tags), adding meaningful links to/from the page (to decent sites) and quality content improves the ranking, pages dedicated to content show up.

Finding old links should be fairly easy,
site:http://www.oldsite.com
as a Google query should return you most of them, google analytics should help return the others if you have a default 404 that logs request urls etc