Is it necessary to have the intention overnight (prior to the act) for Wudu and prayer, or is it sufficient to go to the restroom or the mosque for the intention of each?

It is not obligatory to bring to mind or to utter the intention when going to the bathroom or the mosque. The place of intention is the heart, and its time is the beginning of the action. Uttering it is not a condition. Intention follows knowledge; whoever knows what he intends to do, intends it without choice. Every action performed by a sane, consenting person must have an intention. Whoever suffers from obsessive whispers regarding intention should know that it is impossible to perform an action without an intention, and he should ignore these whispers.