The Islamic Law is like The Law Lite 2.0. The Islamic Shari'ah is a bit less strict on things than the Jewish Halacha. Like the example you gave about seven ritual days after the cessation of menses...the Islamic Law is less strict on this matter, and says only during the time of menses, not any days after that. And there are also other issues I've seen where the Islamic Law is less stringent than the Jewish Law.
We actually believe that when Prophet Muhammad [s] made The Ascent to meet His Lord Most High, he [s] also met the soul of Prophet Moses [as] in the heavens. Prophet Moses [as] instructed Prophet Muhammad [s] to beg God Almighty to make the Law less strict on the nation of Muhammad [s], because Moses [as] said that the Law broke the backs of the Children of Israel; Moses [as] said that out of his own experience with his own nation [the Children of Israel], the nation of Prophet Muhammad [s] would not be able to bear it. So Prophet Muhammad [s] implored God Almighty for mercy on this matter, and God Almighty accepted it of him. Initially, the Muslims were instructed to pray fifty times a day, instead of five. But God granted the Muslim nation lenience and promised to count each prayer as equal to ten. Prophet Muhammad [s] narrated the story:
"God had fixed fifty prayers for my nation. But on my journey (back), I happened to pass by Moses [as]. He inquired, 'What has God made obligatory for your nation?' I said, 'Fifty prayers.' He [Moses] said, 'Go back to your Nourisher because your nation will not bear it.' I returned and got its number reduced from my Nourisher. Then God eliminated half of its number. When I returned to Moses [as], I said to him, 'Half of the prayers have been eliminated.' He [Moses] then said, 'Go back again to your Nourisher. Your nation would not even be able to bear this.' I got it further decreased from God. God pronounced, 'Five prayers are kept obligatory and these are equal to fifty in reward. There is no change in Our pronouncement.' After that when I returned to Moses [as], he said, 'Go back again to your Nourisher now.' I said, 'Now I feel (too) ashamed of my Nourisher (to go back).'" (Sahih al-Bukhaari)