Learn Italian: Non ho la certezza che questa leva apra la porta. - I am not certain that this lever opens the door.

The phrase non ho la certezza che expresses a lack of certainty. In Italian, negative statements of certainty introduce doubt, which triggers the subjunctive mood in the dependent clause. This is why the verb aprire takes the subjunctive form apra.

Would I still use the subjunctive if the sentence was affirmative?

No. If you drop the non to say ho la certezza che (I am certain that), you are stating a fact with no room for doubt. You would then use the normal indicative mood: Ho la certezza che questa leva apre la porta.

Is it just as common to use an adjective here, like Non sono certo che?

Yes, both are very natural. Non sono certo che (I am not certain that) and Non ho la certezza che (I do not have the certainty that) mean exactly the same thing. Because both express doubt, they both require the subjunctive in the second part of the sentence.

Why does the verb aprire end in -a here instead of -e?

In the present subjunctive, regular verbs ending in -ere and -ire take an -a ending for the first, second, and third person singular. Since the subject of this clause is questa leva (third person singular), the correct subjunctive form is apra.