Question

1. He looks in his diary and sees the wrong data.

(Do we have to use the preposition 'in'? How about 'looks at'?)

2. Fix uses a warrant to arrest Fogg.
3. Fix uses a document to arrest Fogg.

(Is 'a warrant' a document? Can we substitute 'a paper' for 'a warrant'?
Is a warrant 'a document'?)

Answer 1

1. Either "in" or "at" is fine.

A warrant is a document, but not just any document. Referring to an arrest, no other word will carry the same meaning. Only #2 works for this purpose.