How to Do Ghusl after Period
Question

I do ghusl following menses as follows: 
1- I form the intention to purify myself in my heart, without uttering it out loud.
2- I start by standing beneath the shower and letting the water flow all over my body.
3- I wash my entire body using a loofah and soap, including the private parts.
4- I wash my head using shampoo
5- After that I rinse all traces of soap and shampoo from my body and I let the water flow three times over the right side of my body and three times over the left side
6- Then I do wudu. 
Recently I found out that I am not following the correct steps of ghusl. I hope that you can advise me whether the ghusl I have been doing all these years as described above is wrong or correct…
If it is wrong, then I hope you can tell me what I should do to correct this mistake which I have done repeatedly for years. Are my prayers and fasts during this time invalid and not accepted? If that is the case, what can I do to set things straight? I also hope that you can tell me the correct way of doing ghusl in the case of menses and janabah.
Praise be to Allah.Types of ghusl
Your ghusl in the manner described is valid and acceptable, praise be to Allah. But you have missed out some of the sunnahs, which does not affect the validity of your ghusl. 
The reason for that is that ghusl is of two types: acceptable and complete. 
Acceptable ghusl
In the case of acceptable ghusl, it is sufficient to do the obligatory parts of ghusl only, without doing any of the mustahabb or Sunnah actions. He should intend to purify himself, then make water reach every part of his body, using any means whether that is standing beneath a shower or immersing oneself in the sea or in a swimming pool and the like, as well as rinsing the mouth and nose.  
Complete ghusl
Complete ghusl means doing what the Prophet (peace and blessings of Allah be upon him) did, with all the sunnahs of ghusl. 
How to do ghusl
Shaykh Muhammad ibn ‘Uthaymin was asked about how ghusl is done. 
He replied: Ghusl may be done in two ways: 
·        By doing the obligatory parts of ghusl only, which is making water reach all parts of the body, and includes rinsing the mouth and nose. If a person makes the water reach all parts of his body, by whatever means, then he has removed the major impurity and purified himself properly, because Allah says (interpretation of the meaning): 
“If you are in a state of Janabah (i.e. after a sexual discharge), purify yourselves (bathe your whole body).” [al-Maidah 5:6]
·        The complete way, which is doing ghusl as the Prophet (peace and blessings of Allah be upon him) did it. When he wanted to do ghusl in the case of janabah, he would wash his hands, then wash his private part and anywhere else that the impurity had reached, then he would do complete wudu, then he would wash his head three times with water, then he would wash the rest of his body. This is how complete ghusl is done.” (Fatawa Arkan al-Islam, p. 248) 
How to do ghusl after a period
There is no difference between ghusl in the case of janabah and ghusl following menses except that it is more mustahabb to rub the hair in the case of ghusl following menses than in the case of ghusl following janabah . It is also mustahabb for the woman to apply perfume to the site of bleeding, to remove any unpleasant smell. 
Muslim (332) narrated from ‘Aishah (may Allah be pleased with her) that Asma asked the Prophet (peace and blessings of Allah be upon him) about ghusl following menses. He said: “Let one of you take her water and lotus leaves and clean herself well, then let her pour water over her head and rub it vigorously so that it will reach the roots of her hair. Then let her pour the water over herself, then take a piece of cloth scented with musk and purify herself.” Asma said: How should she purify herself? He said: “Subhan-Allah! Purify yourself with it.” ‘Aishah said – as if she whispered it to her – Follow the traces of blood. And she asked him about ghusl in the case of janabah. He said: “Let her take water and clean herself well – or clean herself thoroughly – then let her pour water over her head and rub it so that it reaches the roots of the hair, then let her pour water over herself.” ‘Aishah said: How good the women of the Ansar were! They did not let shyness prevent them from understanding their religion properly. 
So the Prophet (peace and blessings of Allah be upon him) differentiated between ghusl following menses and ghusl following janabah, with regard to rubbing the hair and applying perfume. 
Saying Basmalah in wudu and ghusl
Saying Bismillah when doing ghusl and wudu is mustahabb according to the majority of jurists, and the Hanbalis said that it is obligatory. 
Shaykh ibn ‘Uthaymin (may Allah have mercy on him) said: 
“Saying Bismillah is obligatory according to our madhhab, as in the case of wudu. There is no text concerning that but they said: It is obligatory in the case of wudu so it is more so in the case of ghusl, because that is a greater purification.  
But the correct view is that it is not obligatory in the case of either wudu or ghusl.” (Al-Sharh al-Mumti’) 
Rinsing mouth and nose in ghusl 
Rinsing the mouth and nose is essential in ghusl, as is the view of the Hanafis and Hanbalis.
Al-Nawawi said, discussing the difference of opinion on this point: the views of the scholars on rinsing the mouth and nose are four: 
·        That these actions are two of the sunnahs of wudu and ghusl. This is our view (Shafi’i).
·        That they are obligatory in both wudu and ghusl and are conditions of them being valid. This is the well known view of Ahmad.
·        That they are obligatory in ghusl but not in wudu. This is the view of Abu Hanifah and his companions.
·        That rinsing the nose, but not the mouth, is obligatory in wudu and ghusl. This was narrated from Ahmad, and Ibn al-Mundhir said: This is my view. (Al-Majmu’, 1/400) 
The correct view is the second one, which is that rinsing the mouth and nose is obligatory in ghusl, and that is a condition of it being valid.  
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: 
“Among the scholars are some who say that ghusl is not valid without them (i.e., rinsing the mouth and nose), as is the case with wudu. 
And it was said that it is valid without them. 
The correct view is the former, because Allah says (interpretation of the meaning): “purify yourselves (bathe your whole body)” [al-Maidah 5:6], and this includes the entire body. The inside of the nose and mouth are part of the body which must be purified. Hence the Prophet (peace and blessings of Allah be upon him) enjoined that in wudu because they are included in the words of Allah (interpretation of the meaning): “wash your faces” [al-Maidah 5:6]. As they are included in washing the face and are included in that which must be purified in wudu, they are also included in ghusl, because purification in that case is even more important.” (Al-Sharh al-Mumti’)
Is ghusl valid without rinsing the mouth? 
If in the past you did not rinse your mouth and nose when doing ghusl because you did not know the ruling on that or because you were following the opinion of someone who does not regard that as obligatory, then your ghusl is valid and your prayers offered following that ghusl are also valid, and you do not have to repeat them, because of the strong difference of opinion among the scholars concerning the ruling on rinsing the mouth and nose, as stated above. 
May Allah help us all to do that which He loves and which pleases him. 
And Allah knows best