Hi Hana,
The Suica card can be used for (nearly) every kind of local transport in Tokyo, the JR, metro and Monorail all appect the Suica card.
The JR Pass covers all JR lines nationwide, including all Shinkansen lines and the JR network in Tokyo. Train types classifiend as Nozomi/Mizuhou are not covered but any other train type, such as the Hikari/Sakura is.
The metro is not part of the JR network and thus requires additional tickets.
Does that clear things up?
Tsukiji is well worth a visit if you can manage to be there before 4:30. This means either taking a taxi or sleeping closeby.
Hope that helps,
Daniel