Although there are no dairy ingredients in vegan cheeses, it is possible that the product was made on dairy equipment and therefore cannot be eaten with meat. A reliable kosher certification will indicate whether or not the vegan cheese is truly pareve and can be eaten with meat.
So long as the non-dairy Vegan cheese is labeled either "pareve" or it does not have a "DE" indicating it was produced with equipment also used for dairy. In many cases if there is a reliable kosher symbol (hekhsher) and it does not have a "D" for dairy (or state "Dairy" outright), it can be assumed that the product is kosher-pareve.
If it is pareve, the non-dairy Vegan cheese could be used with meat and it would be considered kosher. There are some who are concerned about "marit ayin" -- that it would look like a non-kosher dish, so to avoid that concern one should announce that the dish is a meat dish with pareve cheese.
Yes. As long as there is nothing in the ingredients that is a dairy product, then it is not considered dairy, even if it is a dairy substitute. If it is truly vegan and without any dairy products in the ingredients, then it is pareve, and can thereby be considered kosher. There is the concept of mar’eit ayin, concerning perception and how certain things appear to others. In that regard, I am sure there are many who would say this practice should be avoided, particularly in public, as a passerby is unlikely to know whether the “cheese” product on the meat is actually non-dairy vegan, and thereby think you are breaking kashrut. But in the strictest sense of the Torah laws and halacha, as long as the product is not dairy in any way, it can be mixed with meat and still be within the bounds of kashrut.