Answers

If the texture is a sparyed-on or roll-on application, there are strippers which will loosen and allow that to be scraped-off.  If it is drywall mud, it's not coming off so easily and you will spend many hours and create a huge mess sanding that down with an orbital sander... then potentially have to re-skim to get the surface ready to accept a good tile job.

We do a lot of backsplashes in existing homes. When the substrate (the surface to which the tile is to be applied) is not satisfactorily flat and smooth, we find that the quickest, cleanest, simplest solution is to remove the drywall and replace with new, moisture-resistant drywall.