The base that your Mom provided sounds perfect for the purpose and I think your choice as to lighting the charcoal over the sink is very sensible.
Using ground charcoal will work, although it may require a bit of practice - see here
- scroll down to 'Usage for Ground Coal'. Leaving an ash base, as you see there, helps, but I would not retain as much as is shown in the photo, as you want to minimize the risk of overflowing the censer bowl and making a mess (or worse, if there are hot ashes remaining in the base).
A couple of cautions, they seem very basic, but the obvious isn't always:
(1) Be certain to never leave the censer burning when you are out of the house or even if you intend to be out of the room for a prolonged period;
(2) Always dispose of the used ash as if it contained hot coals, as it well may. (An empty one of those 5 pound popcorn tins - kept outside, away from the house, and with its lid on - works great for this purpose, just as metal 'ashcans' - what we now call garbage cans - did back in the day when coal was the principal heating fuel.)