What would the written language have been like during the time of Moses (I'm assuming that to be around 1400 BCE), and what kind of material would they have been writing on - was it all on stone tablets or would Papyrus have been used?
There was lots of writing going on in the second millennium BC; The Egyptians were writing in Egyptian on papyrus and stone; the Babylonians were writing in Akkadian on clay tablets and on stone; the people of Ugarit were writing in Ugaritic; the Hittites in Hittite; the Greeks in Mycenean Greek, and so on.
The dating of Moses to around 1400 BC goes back to the Seder Olam, a Jewish work from the end of the 1st century AD, the author of which decided arbitrarily that the Exodus took place exactly 1000 years before the beginning of the Seleucid era (the system of time-keeping generally in use in Asia in the Roman period). This dating has no historical basis. For this reason, your question about what language was being written (where?) at the time of Moses (when?) cannot really be answered.
Here is a link to the new edition of the Seder Olam: https://www.eisenbrauns.com/ECOM/_4560IPGBF.HTM
Lester L. Grabbe says in Ancient Israel, page 117 that there were no pre-eighth century alphabetic writings in the area of Israel and Judah, except for the Gezer calendar which was probably Canaanite, early Hebrew and Canaanite writings being very difficult to distinguish. The spread of alphabetic writing did not antedate the mid-eighth century and not a single inscription has been found in Jerusalem before the late eighth century. The development of the Hebrew language has persuaded most scholars that it evolved from a dialect of Canaanite in the ninth century. This takes us back to the Amarna letters from the mid-1300s, including those from the Canaanite king of Jerusalem. These were written in poor Akkadian, since this was a language the Egyptian overlords would understand, whereas Canaanite was a poor substitute (Lawrence E. Stager, 'Forging an Identity: The Emergence of Ancient Israel', published in The Oxford History of the Biblical World, page 47.) The Canaanite kings and their literate elite would certainly have written to each other in Canaanite, the language they spoke.
If we accept the dominant scholarly view that the original Israelites were actually a rural subset of the Canaanites (eg Stager, page 102), then the few literate persons among them would have used Canaanite, which gradually emerged in Israel and Judah as the Hebrew language.
The Sumerians were a non-Semitic, non-Indo-European people who lived in southern Babylonia from 4000-3000 B.C.E. They invented cuneiform writing, and their spiritual beliefs influenced all successive Near Eastern religions, including Judaism, Christianity and Islam. They produced an extensive body of literature, among the oldest in the world. Historically, the decipherment of Sumerian resulted from that of Akkadian, which in turn followed the decipherment of cuneiform Persian. In addition to the economic and historical material described above, there is also a varied and important group of tablets inscribed with lexical and mathematical texts and with incantations. 11 But by far the most significant material for the study of Sumerian culture, especially in its more spiritual aspects, consists of a group of "literary" tablets dated about 1750 B. C. which are inscribed with Sumerian epics and myths, hymns and lamentations, proverbs and "words of wisdom." The great city of UR Abraham was born in 2166 BC. ‘Thus says the Lord, the God of Israel, “From ancient times your fathers lived beyond the River, namely, Terah, the father of Abraham and the father of Nahor, and they served other gods”’ (Joshua 24:2).Sumerian was spoken in Sumer in southern Mesopotamia (part of modern Iraq) from perhaps the 4th millennium BC until about 2,000 BC, when it was replaced by ****Akkadian**** as a spoken language, though continued to be used in writing for religious, artistic and scholarly purposes until about the 1st century AD. Sumerian was still being studied in scribal schools and even chanted in liturgy through the Persian and Hellenistic periods. Religious belief's state the Tower of Babel changed God's one language into many different languages which would date around 4000 BC. Then again, Jewish tradition as well as some Christian Scholars, believed that Hebrew was the original language of man (William Smith, "Hebrew Language," Smith's Bible Dictionary, 1948 ed.: 238). The first mention of a Hebrew is in Genesis 14:13 where Abraham is identified as a "Hebrew" (Eevriy in Hebrew). In Exodus 2:6 Moses is identified as one of the "Hebrews" (Eevriym in Hebrew) and throughout the Hebrew Bible the children of Israel are often identified as "Hebrews." A "Hebrew" is anyone who is descended from "Eber" (Ever in Hebrew), an ancestor of Abraham and Moses (See Genesis 10:24). The northern Kingdom of Israel was taken into captivity by the Assyrians around 740 BC and the southern Kingdom of Judah was taken into Babylonian captivity about 570 BC. During their captivity in Babylon, the Hebrews continued to speak the Hebrew language, but instead of writing the language with the Hebrew script (often referred to as Paleo-Hebrew), they adopted the ****Aramaic**** square script to write the Hebrew language and the Hebrew script was used on a very limited basis such as a few Biblical scrolls and coins.
When the Hebrews returned to the land of Israel, around 500 BC, it was believed that the Hebrews had abandoned the Hebrew language and instead spoke the Aramaic language, the language of their captors in Babylon. We know Jesus spoke Aramaic.In the Diaspora, the earliest Jewish inhabitants of Alexandria in the fourth century B.C.E., to judge from the papyri, spoke Aramaic; but so thorough going was the victory of the Greek over the Hebrew language that after the third century B.C.E., with the exception of the Nash Papyrus, until 400 C.E., all papyri from Egypt pertaining to the Jews are in Greek. In 1948, Hebrew became the official language and, once again, Hebrew became the native language of the Hebrew people. Origen once stated, "Only God Knows." What language did Moses speak? According to Jewish records, Hebrew Hebrew flourished as a spoken language in the Kingdoms of Israel and Judah during about 1200 to 586 BCE. Moses would have been taught the language of Ur which would have been ancient Sumerian, Hebrew, Aramaic, and possible Greek, which I doubt the latter. God speaks in All Languages...
Moses spoke Egyptian as a first language, and then later on he spoke Hebrew. It is not clear exactly where he learned Hebrew because the Bible does not state him clearly speaking Hebrew. He most likely spoke to his mother, brother and sister in Egyptian because it was the duty of a slave to speak Egyptian not the other way around.
It's believed Moses became extremely interested in learning Hebrew when he left Egypt. It's believed that he picked up the language when he was out of Egypt working as a shepherd.
The myth that early forms of Hebrew writing developed around the 8th century B.C., and scribes wrote the Torah in the 6th century B.C. has been debunked by archeological finds in the last 8 years. Hebrew writing has been found from at least as far back as the 10th century BC, around the time of King David. Source:https://www.livescience.com/8008-bible-possibly-written-centuries-earlier-text-suggests.html For the Hebrew alphabet to be in use as fully functional at that time, it had to have been developed earlier. It takes time for a system of writing to be learned and understood. We can safely assume that Hebrews were writing well before this. There’s no reason to think that Moses couldn’t possibly have written the Torah. Just because evidence of Hebrew writings the time of Moses hasn’t been found yet, doesn’t mean it doesn’t exist. Secular archeologists and historians have often argued that cities or people groups mentioned in the Bible didn’t exist...until they were found, and those people move on to the next thing to “discredit” the Bible.