What is the ruling on my suffering from intrusive thoughts regarding the intention (niyyah) and the opening takbir (takbirat al-ihram), and doubts about the validity of istinja' (washing after relieving oneself) after answering the call of nature?

There is no cure for the whispers of urine drops except to completely disregard and ignore them, and not to rule that anything has exited except with absolute certainty. When performing ablution and prayer, bring the intention to your heart, then begin immediately without stopping, and do not pay attention to Satan's whispers regarding the intention or the Takbir.