Shalom and thank you for your question! I also do not know what the Sharia (Islamic law,) has to say about depictions of G-d, but I do know that Jewish law does not endorse it, and this is for a simple reason. Maimonides, (known by the acronym Rambam,) twelfth century codifier of Jewish law, teaches us that G-d does not take on any sort of form, “He has no body and no semblance of a body.” There is no physical form of G-d, and therefore it is not possible to make any sort of image of HIm.
When we say “Him”, by the way, G-d has masculine and feminine manifestations. In certain contexts, like in the prayer book or the Bible, or a conversation such as this, we refer to the masculine manifestation. The “Divine Presence” however, that is said to rest in holy places or in a group of people learning Torah, or amongst a married couple living in marital harmony, is a feminine manifestation, or type of energy.
Truly, Kabbalistic and Chassidic teachings explain that G-d is so infinite, that it is not possible for the human intellect to comprehend Him, and certainly not to limit Him by using definitions. When the Bible uses human expressions such as love or anger with regard to G-d, the Sages of the Talmud explain that the Torah uses a language form that humans can relate to, but it is only for the sake of understanding the interactions on the human end, not as a way of understanding G-d. We believe G-d is far removed from all and any definitions.
Have I confused you? I hope not…
You mentioned paintings. Jewish religious art is wide-ranging and ever growing, and as you said, I am not familiar with attempts to portray an infinite G-d. Jewish art focuses on things like Jewish family life, still-lifes of Jewish ritual objects like prayer books and prayer shawls, Jewish people at prayer, candle-lighting… the list goes on. All these are images of G-dliness in the human experience, but not of G-d Himself. This past Chanukah, an interesting work of art was carried out in Siberia, where a Chabad emissary, (an outreach Rabbi,) had a menorah constructed out of ice. It was large, beautiful and impressive, and caused a local Jew to become very moved and to reconnect with his roots.
There are many laws dealing with painting, photography and sculpture, so that we do not transgress the injunction to not make ‘graven images’. This is related to your question, because we believe G-d has no physical form, and we worship only the One G-d and not any ‘graven image’. The story is told that the Biblical king Menashe was reincarnated centuries after his death to atone for worshipping idols and causing the nation to worship them. If I remember correctly he had repented towards the end of his life, but his soul needed to be rectified, so he reincarnated as a pious Jewish artist, who took it upon himself suddenly one night to destroy all the graven images in his town, for which he was duly arrested and put to death, thus bringing about the rectification of his soul.
Judaism believes that the existence of the entire universe is only inasmuch as G-d wills it to be. If G-d should desire to cease the existence of the world, it would just not be there. So in a sense, just to confuse you again, everything we look at is G-d. Nevertheless we believe that the paradox is sustained, and although the entire universe is part of G-d, nonetheless
G-d has no form and no definition, and thus we cannot portray HIm.