Does having sexual intercourse with a menstruating woman and anal sex invalidate prayers for forty days and lead to disbelief (kufr) and expel one from Islam, similar to the ruling on going to a diviner and believing him? And does one need to utter the Two Testimonies of Faith to re-enter Islam?

It is forbidden to have intercourse with a menstruating woman and to have anal intercourse with a woman, as Allah Almighty says: (And they ask you about menstruation. Say, "It is a discomfort, so keep away from women during menstruation. And do not approach them until they are pure. And when they have purified themselves, then come to them from where Allah has ordered you." Indeed, Allah loves those who repent and loves those who purify themselves) Al-Baqarah/222. And as the Prophet, peace and blessings be upon him, said: (Whoever has intercourse with a menstruating woman, or with a woman in her anus, or goes to a soothsayer and believes what he says, has disbelieved in what Allah has revealed to Muhammad, peace and blessings be upon him). And his saying: (Cursed is he who has intercourse with his wife in her anus). And his saying: (Allah, the Mighty and Majestic, will not look at a man who has intercourse with his wife in her anus).

Whoever does this without considering it permissible has committed a grave sin, but he does not exit Islam. The disbelief mentioned in the Hadith (definition) is minor disbelief, not major. And it is obligatory for whoever has intercourse with his menstruating wife to give a Dinar or half a Dinar in charity.

In summary, whoever falls into any of that, let him repent to Allah Almighty and seek His forgiveness. He is not required to renew his Islam unless he considers it permissible despite knowing it is forbidden.