Im glad it's been able to help you visualise your own bathroom, that's kool.
I use an angle grinder with a good quality porcelain specific cutting blade.
On that one in particular I think I used a
Markrist AkkuMAX
They're around £35-40.
The last question is a multiple answer........
All of the above!
I cut the shape first and then polished the porcelain back to achieve the finish. Difficult without the correct equipment and practise. It would depend how good you need the finish, and where the tile was going and what was visible.
If you're able to explain in detail what you want to achieve, maybe we can give you options.