Are there restrictions having surgery during the "Three Weeks" and Tisha b'Av? What are the sources for restrictions/limitations if there any?
All surgery that can safely be postponed until after Tisha B'Av should be postponed. See R. Simcha Bunim Cohen's Halachos for Daily Living, volume on the Three Weeks and Fast Days. Published by ArtScroll.
In Kovetz Halchos(Rav Shmuel Kaminetsky) perek 7:4 : it is better to wait and push off surgery if possible since there is a chance of danger. This is also what Rav Yaakov Kaminetsky paskened in his Emes L'Yaakov siman 551 (haarah 515).
However, Rav Moshe Feinstein paskened one does not need to be particular about this (שמעתתא דמשה,שמועות סימן תקנא סקמ"ב )
This is referring to the 9 days.