The subject is la pioggia, which is third person singular, so the verb must also be third person singular:
Since la pioggia is singular, costringe is the correct form.
Because costringere normally uses the pattern:
costringere qualcuno a + infinitive
So you say:
Without a, the sentence would be incorrect.
Yes, often you could. Tornare and ritornare can both express the idea of returning. In everyday Italian, tornare is extremely common and sounds completely natural.
Depending on the situation, another verb like rientrare might also be possible, but that can suggest returning home or going back inside, so it is not always interchangeable.