Can the USPTO examine claims not requested for reexamination under 35 U.S.C. 302?

Yes, the USPTO can examine claims not specifically requested for reexamination under 35 U.S.C. 302, but this is at the discretion of the Office. According to MPEP 2243:

The decision to reexamine any claim for which reexamination has not been requested under 35 U.S.C. 302 lies within the sole discretion of the Office, to be exercised based on the individual facts and situation of each individual case.

Additionally, the Office can always initiate a reexamination on its own initiative for non-requested claims under 35 U.S.C. 303(a).

To learn more:

Topics: MPEP 2200 - Citation Of Prior Art And Ex Parte Reexamination Of Patents, MPEP 2243 - Claims Considered In Deciding Request Filed Under 35 U.S.C. 302, Patent Law, Patent Procedure
Tags: ex parte reexamination, patent claims, Uspto Discretion