This question has 2 parts. First is about the existence of God and second is about Moses, Jesus, and Muhammad (peace be upon them).
For the 1st part of the question, I will share a link that I wrote already about it. Here it is- Saad’s answer to Does God exist?
For the 2nd part of the question:
Moses, Jesus and, Muhammad (peace be upon them) are prophets of Allah (the almighty).
It is clearly mentioned in the Holy Quran:
“Verily, We have inspired you (O Muhammad) as We inspired Nuh (Noah) and the Prophets after him; We (also) inspired Ibrahim (Abraham), Isma’il (Ishmael), Ishaque (Isaac), Ya’qub (Jacob), and Al-Asbat [the twelve sons of Ya’qub (Jacob)], ‘Iesa (Jesus), Ayub (Job), Yunus (Jonah), Harun (Aaron), and Sulaiman (Solomon), and to Dawud (David) We gave the Zabur (Psalms). And [We sent] messengers about whom We have related [their stories] to you before and messengers about whom We have not related to you. And Allah spoke to Moses with [direct] speech. Messengers as bearers of good news as well as of warning in order that mankind should have no plea against Allah after the Messengers. And Allah is Ever All-Powerful, All-Wise.”-(The Quran 4:163–165).
“Muhammad is not but a messenger. [Other] messengers have passed on before him. So if he was to die or be killed, would you turn back on your heels [to unbelief]? And he who turns back on his heels will never harm Allah at all, but Allah will reward the grateful.”-(The Quran 3:144).
“Muhammad is not the father of [any] one of your men, but [he is] the Messenger of Allah and last of the prophets. And ever is Allah, of all things, Knowing.”-(The Quran 33:40).
“Indeed, Allah confers blessing upon the Prophet, and His angels [ask Him to do so]. O you who have believed, ask [ Allah to confer] blessing upon him and ask [ Allah to grant him] peace.”-(The Quran 33:56).