The idea that there is a single God is called monotheism. Islam is the simplest and pure monotheistic religion.
Muslims believe that there is a single God (Allah or Ishwar). That God has created everything. We are only supposed to pray before that God. Whenever we need help, we call upon God. We do not pray to God indirectly (through any image or idol). When we stand for prayers, we believe that God is listening directly to what we are saying.
The idea that everything is part of God comes from Vedanta School of Sanatan Dharma (or Hinduism). As per this idea, everything in the world is "part" of Brahman (or God). They accept that there is one God. However they find it OK to pray before idol. Since that idol is also part of God. They think it is OK to worship other humans and even ourselves. The ultimate goal is "Mokhsha" - a state where one merges with Brahman and loses his or her sense of identity.
I find some incongruencies in the idea of everything being God. Consider a criminal. For example consider a rapist who rapes someone. God forbid, is a part of God raping another part of God?
Obviously this is not what Hindus would agree with. I am not sure what is the proper response from Hindus to this question. Some of them talk about an "ansh" (part) of God being present inside everyone.
The way I look at it is, everyone is not perfect. To worship a person becomes wrong because of its imperfections. That is why I devote myself to worship of Allah directly.