Is it permissible for one who suffers from obsessive doubts about the the validity of his Islam to declare the Shahada and perform ghusl to ease his conscience, and must the ghusl be performed with lote tree leaves (Sidr) or is water sufficient?

Whoever suffers from waswasah (whispering of Satan/obsessive thoughts) should completely ignore them. What the questioner mentioned about reciting the tashahhud and performing ghusl (ritual bath) to ease her conscience is not a solution; rather, it deepens the problem. As for using sidr (lote tree leaves), it has no connection to ghusl; rather, it is mentioned in the treatment of sihr (magic). No evidence has been reported from the Sunnah confirming or denying the use of seven leaves from it, and we cannot definitively state the existence of a specific marfu‘ (traced back to the Prophet) hadith in this regard.