Vinyl is certainly not as resistant to tears and scratches as ceramic tile is, but most vinyl does have an inner layer built into it now which tends to resist tears quite well. I wouldn’t hesitate to consider it in a high traffic residential area.
We generally recommend that the underlayment be removed because the subfloor may not be adequate to support tile. However, if your existing vinyl floor was installed over an adequate subfloor using a full spread installation method then yes, it can be done if you use the proper installation products.
There are many types of tiles to choose from that provide a high slip coefficient. Keep in mind, the higher the slip coefficient, the more difficult the tile is to clean. Most tiles today offer a nice balance between ease of maintenance and safety.