Do I Have to Remove Old Tiles?

You do not have to, provided the original surface is truly stable and even. It only makes sense to keep old tiles or coverings if there are no hollow areas, de-laminations, grease, or loose grout. The advantage is clear: less demolition, less dust and faster renovation. The downside is that a poorly checked substrate can later result in cracks or detachment. More detailed guidance can also be found in the related article: https://www.design-solution.cz/content/17-betonova-stěrka-na-obklad-dlazbu