Minimum Query Length
I have products indexed whose name begins with VariCel. Searching for "Var" on the Sitecore front end or directly in the Coveo Index Browser never returns results, adding one more character and searching for "Vari" does return results, wondering what the reason behind this might be and whether I can decrease the number of characters required to get results.
There is no minimum length for the free text queries. There are stop words that are not searched like "an", "the", "and". I don't know if "var" is one of them.
The reason why your search for "Vari" does return results is probably that one of the field, the title, the URL or the text body of the item contains the standalone term "vari". You can check the fields section in the index browser for one of the returned result. Type "vari" in the filter box above the list of fields and you will see all the fields that contains the term.