Does one sin if he prays Fajr while doubting whether he is in a state of major ritual impurity (janabah) due to a wet dream, of which he is not certain?

The correct approach is to ignore the waswas (whispers of Satan or obsessive thoughts) and not pay attention to it. If you doubt a wet dream, the original state is purity. As for drops of urine, if it is waswas, then do not pay attention to it. But if you are certain of it and it reaches the level of incontinence (sals), then you must take precautions and perform ablution (wudu') after the time for prayer begins, and pray with that ablution, while purifying whatever has affected the body and clothes. It is permissible for someone afflicted with waswas to adopt the Maliki school of thought for ease.