Questions & Answers about Speriamo che lui valuti bene la sua agilità.
Why is lui explicitly stated here instead of just saying Speriamo che valuti?
In the present subjunctive, the conjugations for io, tu, and lui/lei are identical. For a regular -are verb like valutare, all three singular forms are valuti. Including lui clarifies exactly who is doing the evaluating.
Why is the verb valutare conjugated as valuti with an -i ending?
It is in the present subjunctive mood. The verb sperare (to hope) expresses a wish or expectation, which triggers the subjunctive in the dependent clause after che. For -are verbs, the singular present subjunctive ending is -i.
Could we use the infinitive here and say Speriamo di valutare?
Not with this meaning. You only use di plus the infinitive when the subject of both verbs is the same, which would mean we hope that we evaluate. Because the subjects in this sentence are different (we hope vs he evaluates), you must use che plus the conjugated subjunctive verb.
Is the article la required before sua agilità?