Diabetes is described in the the Ebers Papyrus (from c. 1550 BCE, themselves copied of earlier texts), by Sushruta and Charaka (Indian doctors from 5th and 6th century BC) and the Huángdì Nèijīng, from the late Warring States period and the Western Han dynasty.
Likewise, a 1.7 million year old osteosarcoma was found in 2016, and the Edwin Smith Papyrus, written around 1600 BC (possibly a fragmentary copy of a text from 2500 BC), described instances of cancer and how to cauterize breast tumors. Hippocrates himself coined the name "cancer"
Finally, the term “autism” was coined in 1911 by Eugen Bleuler and what we could describe as autism was first studied by Grunya Sukhareva starting in the 1920s. Earlier cases, such as the so-called changelings, have been described.
In contrast, modern vaccination started with smallpox in 1796. More vaccination appeared at the start of 20th century.
So there’s no link between vaccination and the medical issues you listed.