Doubt about having done ghusl correctly. Will I have to repeat my fasts and prayer?

[Dumbledore]

I did ghusl near the beginning of Ramazan after menses and started praying and fasting. However, I have learnt last night that I might have not done ghusl correctly since I might have doubt about letting water run through all parts of my body.

I also have a question regarding niyat of ghusl. If I went into the bathroom with the thought of doing ghusl and praying, but then showered using a soap which might have haram ingredients(I was unaware of it at the time), did not make niyat again and washed my body after washing off the soap, will my ghusl be in order?

My second question is: If the ghusl is not in order, will I have to repeat all my fasts and prayers(salat) for the previous days?

The final question I have is: After something which made ghusl obligatory, I did not perform ghusl and continues with fasts and prayers. At the time, I did not know that ghusl was obligatory for that. But I have recently come to know that I have not performed ghusl where it was obligatory. Will I have to make up for the prayers and fasts I did without doing the ghusl?

(I would be happy if you could provide hadheeth to support the answers)

Thankyou

[abuhajira]

sister, you are a shafi'i, inshALlah I hope some shafi'i learned person would attend to you.