Learn Italian: Sospetto che Marco legga il mio diario. - I suspect that Marco is reading my diary.

Sospettare (to suspect) expresses doubt or a personal belief. Verbs of opinion, belief, and doubt trigger the subjunctive mood in the clause that follows che. That is why we must use the subjunctive form legga rather than the standard present indicative legge.

Why does an "-ere" verb like leggere end in "-a" here?

In the present subjunctive, regular -ere and -ire verbs take an -a ending for all three singular subjects (io, tu, lui/lei). A helpful trick for the present subjunctive is to remember that the vowels swap compared to the normal present tense: -are verbs take -i, while -ere and -ire verbs take -a.

Could I use the infinitive and say Sospetto leggere...?

Not in this sentence, because the subjects are different: I am suspecting, but Marco is doing the reading. You only use the infinitive (usually combined with di, as in Sospetto di leggere...) when the subject of both actions is exactly the same person.

Just as a refresher, why do we need il in il mio diario?