Authenticity cannot be settled on a video call. In this trade "fake" covers several different things — dyed, heat-treated, glass, or a piece assembled from parts — and they are worth asking about separately.
What to ask them to show
It on a scale, on camera, with the reading visible. Weight is the cheapest piece of real evidence in this category.
It under strong light, from behind if it is translucent. Ask them to move the light rather than the stone.
The fractures and the base, close up.
It in or under water, which changes how a surface reads and takes a seller ten seconds.
Three direct questions: has it been dyed, has it been heated, and has anything been glued or assembled? Ask them as three questions, not one.
What a refusal means
"It is completely natural" answered quickly, with no willingness to show the base or the fractures, is the pattern to watch.
A seller who deals in minerals knows that treatment is normal and disclosable. Someone who treats the question as an insult is either inexperienced or hoping you will not press.
What this page will not do
It will not tell you how dye looks in a fracture, how to identify glass by eye, or the correct density of any species. Those are identification skills, they are specific, and a buyer applying a half-remembered version of them to a photograph is not safer than a buyer who knows they cannot tell.
What protects you if you get it wrong
Glass sold as quartz, or a dyed piece sold as natural, is not as described: returnable for 7 days whatever the store's policy says, and reportable.
Questions people ask
Is a treated stone a fake?
No. Treatment is ordinary and has to be disclosed. An undisclosed treatment is the problem.
Is a cheap piece worth asking about?
Scale the questions to the price. For a small specimen, the weight and one honest answer about treatment is plenty.
What about chipping in the post?
That is the real risk here rather than authenticity. Ask how the points and corners will be protected.
More: spotting a counterfeit before you bid, Metzee's position on counterfeits, reporting a seller, questions to ask before bidding on a mineral.