Do the intrusive thoughts (waswas) that precede the takbīrat al-iḥrām (the opening Allāhu akbar of prayer) and make the worshiper feel as if he is intending for other than Allah affect the validity of the prayer, and what is the way to get rid of intrusive thoughts related to intention, and the delaying of fulfilling a need, performing ablution (wuḍūʾ), and ritual bathing (ghusl)?

"Waswasah" (whispers/obsessive thoughts) is one of the most dangerous afflictions, and its only cure is to ignore it and pay no attention to it. If you intend to pray, make your intention sincerely for Allah, then immediately say the opening "Allahu Akbar" (Takbirat al-Ihram (definition)), and do not pay attention to the whispers of Satan. If you relieve yourself, perform istibra' (ensuring no drops remain), then quickly stand up. If you want to perform ablution (Wudu'), wash each limb once, twice, or thrice, and do not exceed that. Turn away from these whispers until Allah cures you of them.