For example, if the host has a Shiny Charm, but I don't, and I join that Max Raid Battle made by the host, will I have the increased shiny rates?
Source
Max Raid dens are not impacted by Shiny Charm, and have an unchangeable 1/4096 odds. Dynamax Adventures in the DLC have 1/100 odds with Shiny charm and 1/300 without.
Hope this helps!