Is the feeling of not grieving due to intrusive thoughts and doubt in Islam, while maintaining prayer, considered disbelief, and how can a Muslim know the state of their faith?

You are a Muslim as long as you bear witness that there is no god but Allah and that Muhammad is the Messenger of Allah. So, do not doubt your Islam, and do not pay attention to the whispers of Satan that corrupt your religion and your worldly life. These whispers do not harm you, and you hate and detest them. Therefore, strive against them by ignoring them. You are on the right path as long as you are striving against them and seeking to get rid of them.