1. The first known algebraic equations known were from the Greek mathematician, Diophantus. Hindu culture is also credited with advancing algebra through Aryabhatta and numerous other mathematicians long before Islamic scholars. If algebra is defined as the application of arithmetical operations to both rational and irrational numbers or magnitudes, then the Indians are the true inventors of algebra. The Persian Mathematician Al Khwarizmi formalized the math already extent, and either way, the Arabs took custody of Indian and Greek science.
2. Ancient medicine was derived by the father of medicine, an unknown Arab named Hippocrates. “Modern” medicine using the “scientific method” was practiced in India for centuries prior to being translated to Arabic. The Arabs equally applied themselves to the study of poisons. They did expand this area of knowledge quite dramatically.
3. The compound bow (using pulleys) was not invented by Islam—it is thoroughly modern in origin. The Composite Bow was invented in Asia, hundreds of years before being picked up by scavenging Arabic hordes.
4. I suppose that may be so. It sounds like another improvement of existing invention.
5. Astronomy predates Islam by millennia. And their “navigation” improvements were detailed in the Astrolabe post.
6. While Western Europeans were first introduced to this material around the 3rd-4th centuries from the historical trading center of Damascus, in present-day Syria. However, its technical and physical origins were from India. Again, an appropriated technology.
Three of the “inventions” stand out as Islamic in nature: The astrolabe—needed to submit to the requirement for prayer. Then , of course, the Bow and the Sword to kill the infidel. Islam has produced generations of killers and they have always esteemed weapons.
Left off your list , yet truly of note was the Islamic invention of the assassin and the suicide bomber—no other culture has ever so applied themselves to the spread of terror and death. Vlad II of Wallachia was also a renowned, if reluctant, student of Islamic techniques. Such dedication and innovation should not be lightly dismissed.
You used Hindu-Arabic numerals to begin each point.