Q4. Assertion: a sensitive instrument placed inside a closed metal box is protected from external electric fields. Reason: the field in a charge-free cavity of a conductor is zero whatever the field outside. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: this is electrostatic shielding (NCERT page 64).
Q5. Two points A and B are on the surface of a charged metal object of irregular shape. Is there a potential difference between them? Is the field the same at both?
No potential difference: the whole conductor is at one potential (NCERT page 62). The field need not be the same: E = σ/ε0 (NCERT Eq. (2.35), page 63), and σ can differ from point to point on an irregular surface; NCERT Figure 2.18 (page 64) shows σ > 0 and σ < 0 on one body.
Q6. A neutral metal sphere is placed in a uniform external field. Where do the induced charges appear, and what is the field inside the metal?
On the outer surface; the field inside the metal is zero, because the induced charges set up a field that cancels the external one inside (NCERT pages 62, 64 and 65).