Not that I am crossing swords with you but a few points to keep in mind:
(1) Islam is not monolithic. There are many attitudes towards prayers and teaching among different Muslim sects.
(2) Muslims do have a high level of providing of instructions (I am interpreting that you intended
teachings to mean
providing instructions), the nature of which differs depending on social context and the level of literacy of the instructor/instructed, ranging from rote repetition of the Quran and the instructor’s interpretation (say, as in a remote Pakistani madrasah) all the way to a critical debate on the role of Islam in an open society (say, as in a pre-Trump American suburb mosque).
(3) Muslims do have an extensive range of prayers, perhaps more than even Catholics had until recently. Today, I see as many hands raised in prayer as I see the perfunctory crossing of oneself among players before an EPL football match. Whether you wish to argue about the prayers (& all other prayers by Muslims in all hours of the day) are really heartfelt or not (only mere ritualism) from your point of view, I think it is only fair to give their sincerity the benefit of the doubt as much as wouldn’t like my sincerity to be questioned when seen to cross myself.
I could be nitpicking here 

(4) According to the Quran, Isa was given the Gospel (singular) not the Bible. But I don’t think this point detracts from your argument.
(5) I always take pain to distinguish Islamic teachings from Muslim teachings. Because, other than the belief in the Oneness of God, the five pillars and the centrality of the Quran (but not the interpretations) I am not sure what Islam teaches. Yes, there are the 6 principles of faith (
iman) but there are just too many groups with differing views that it is difficult for my limited mental capacity to discern a consensus of what they mean other than broad ones subscribed to a majority of Muslims. Not only is there no single Magisterium, there is also no detailed Nicene Creed (other than the 3 points I mentioned above) against which a Muslim can be evaluated - basically if a person declares himself a Muslim, he is accepted as one until proven otherwise. Muslims are generally reluctant to excommunicate another Muslim even though the process (
takfir) exists but only became in vogue recently - even then, most Muslims were reluctant to declare ObL as consigned to hell after 911.
So what does Islam teaches I am not sure. Enough uncertainty for me to avoid presenting any view as orthodox Islam as there will be someone who will pop up who avow an alternative view while still claiming to be an authentic Muslim. In Christianity I can still qualify myself to refer to Nicene Christianity. That is why I will only debate with Muslims but not Islam itself.