Can We Touch Private Parts during Fasting?
Question

I am a young man and got married during the month of Ramadan. When my wife has her period, she asks me to masturbate her with my hand when I am fasting. Is this permissible, so long as I avoid touching the menstrual blood which is impure?
Praise be to Allah.Masturbation by husband’s hand in Ramadan
If the wife is menstruating, she does not have the right to be masturbated by her husband’s hand, because that involves touching the impurity, unless that is done from behind a barrier. 
If the husband is safe from touching the impurity, then there is nothing wrong with it. 
Kissing wife while fasting
There is nothing wrong with the husband kissing his wife , touching her and being intimate with her, without having intercourse, when he is fasting. Prophet Muhammad (blessings and peace of Allah be upon him) used to kiss his wife when he was fasting , and he used to touch his wife when he was fasting. 
But if he fears that he may end up doing that which Allah has prohibited to him, because he is easily aroused, then it is disliked for him to do that. If he ejaculates, then he must refrain from eating and so on for the rest of the day, and he must make up for that day’s fast. As for madhi, that does not invalidate the fast. 
It is permissible for a man to enjoy intimacy with his wife when he is fasting , so long as he does not have intercourse or ejaculate. 
If you are confident that you can avoid touching the impurity, and there is no fear that you will have intercourse with your wife or ejaculate without having intercourse with her, whilst you are fasting, then there is nothing wrong with you doing that. 
Control your sexual desire 
What should be done – indeed must be done – in the case of someone like you, a young man who is recently married, is delay that until night-time, because the ability of a young man to control himself or control his desire is limited , and matters are very likely to get out of hand, in which case you would end up doing something that is prohibited and you would render your act of worship invalid. 
Therefore, when the Mother of the Believers `Aishah (may Allah be pleased with her) narrated that the Messenger of Allah (blessings and peace of Allah be upon him) used to kiss his wives and touch them when he was fasting, she followed that with a statement that there was no fear in the case of the Prophet (blessings and peace of Allah be upon him) that matters would get out of hand or that he would do that which is prohibited. 
Al-Bukhari (1826) and Muslim (1106) narrated that `Aishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) used to kiss and touch (his wife) when he was fasting, but he was the most able of you to control his desire. 
An-Nawawi (may Allah have mercy on him) said: 
Ash-Shafi`i and his companions said: 
“Kissing one’s wife when fasting is not prohibited for one whose desire will not be provoked, but it is better for him not to do that. But it cannot be said that it is makruh for him; rather they said that it is contrary to that which is preferable in his case, even though it is proven that the Prophet (blessings and peace of Allah be upon him) used to do that, because in his case (blessings and peace of Allah be upon him) there was certainty that he would not go beyond the limit of kissing, whereas in the case of others there is the fear that he will go beyond that limit, as `Aishah said: “but he was the most able of you to control his desire.” 
In the case of one whose desire will be provoked, it is haram for him, according to the more correct view of our companions. And it was said that it is makruh. al-Qadi said: A number of the Sahabah and Tabi'in, and Ahmad, Ishaq and Dawud, stated that it is permissible for one who is fasting in all cases. Malik regarded it as makruh in all cases. Ibn ‘Abbas, Abu Hanifah, ath-Thawri, al-Awza‘i and ash-Shafi‘i said it is makruh for a young man but not for an old man. This was also narrated from Malik. Ibn Wahb narrated from Malik (may Allah have mercy on him) that he regarded it as permissible during a supererogatory fast but not during an obligatory fast.                                    
There is no difference of opinion concerning the fact that it does not invalidate the fast unless the individual emits maniy as a result of kissing.” (Sharh Muslim by an-Nawawi) 
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said: 
“That is indicated by the fact that it is permissible for the one who can control himself, but not for the one who is not certain that he will not fall into that which is prohibited.” (Fath al-Bari) 
Moreover, the concession allowing intimacy with a wife who is menstruating is also limited by the condition that the husband be confident that he will not fall into that which is not allowed or that which Allah has prohibited. 
Al-Bukhari narrated in his Sahih (296) that `Aishah (may Allah be pleased with her) said: When one of us was menstruating, if the Messenger of Allah (blessings and peace of Allah be upon him) wanted to be intimate with her, he would tell her to wrap something around her waist, then he would be intimate with her. 
She said: and who among you can control his desire as the Prophet (blessings and peace of Allah be upon him) used to control his desire? 
The practice of the Prophet (blessings and peace of Allah be upon him), as reported in the hadith of `Aishah mentioned above, and similar reports, was to be intimate with his wife from above the waist wrapper that she tied around herself, which is something that covers the area between the navel and the knee, or from above something that covered her private part, if the period had gone on for a long time and the bleeding had become less. 
In fact a number of scholars are of the view that it is haram to be intimate with a menstruating woman involving the area between the navel and the knee, except from above the waist wrapper. This is the well-known view narrated from Malik, Abu Hanifah and ash-Shafi`i.” (Fath al-Bari by Ibn Rajab (2/27 ff) 
And Allah knows best.