Hi, I’m a Muslim so lets me see if I can answer ur questions
1) the answer to ur first question is we worship Allah and not Muhammad, we believe that there is only one God and that Muhammad (peace be upon him) is His last and final messenger and that Muhammad was a human being just like you and me, He was also ordered by Allah to say in the Quran in chapter 18 verse 110: « Say, "I am only a man like you, to whom has been revealed that your god is one God. So whoever would hope for the meeting with his Lord - let him do righteous work and not associate in the worship of his Lord anyone. »
2) Thé answer to ur second question, Nooo it’s not cool to kill people unjustly in the Quran is that’s « Say, "Come, I will recite what your Lord has prohibited to you. [He commands] that you not associate anything with Him, and to parents, good treatment, and do not kill your children out of poverty; We will provide for you and them. And do not approach immoralities - what is apparent of them and what is concealed. And do not kill the soul which Allah has forbidden [to be killed] except by [legal] right. This has He instructed you that you may use reason » Quran 6:151
3) And lastly ur question about the moon, so our holidays area according to the lunate calendar that’s why, and if you are also wondering about the crescent moon being the symbol of Islam, well, it actually isnt the symbol of Islam, there is no symbols islamically the origin of the créant moon representing Islam started when the Ottoman Empire, (The crescent of the new moon signifies the beginning and end of fasting during Ramadan. However, this symbol did not originate with Islam; it was adopted for the first time by the city of Byzantine (which later became Istanbul).)
I hope everything is clear now and if you have any more questions I would rly like to try and answer them 👍👍
Nov 21, 2021