Am I obligated to perform the Prayer of Repentance due to intrusive thoughts of mocking religion, lying about it, and ignoring it, which I sometimes invoke, even though I do not desire them and feel guilty, and knowing that these intrusive thoughts appeared after intrusive thoughts of death?

Whoever experiences obsessive whisperings (waswasah) should completely disregard them. The hatred of waswasah is a sign of sound faith, and the cure for waswasah is to completely ignore it. The prayer of repentance (Salat al-Tawbah) is prescribed, as there are authentic hadiths regarding it. Furthermore, a person experiencing excessive waswasah should frequently seek refuge from polytheism (shirk) and seek forgiveness for it by reciting the well-known supplication: "O Allah, we seek refuge in You from knowingly associating anything with You, and we seek Your forgiveness for what we do not know."