Most stokers are similar in operation. I will see if I an answer some of your concerns.
Piping, You can probalby put a another TEE with a cap in were it goes horizontal into your chimney, for easier clean out. Burning most types of coal will produce the fly ash as you mention. There is nothing around that. A good Shop vac with a good filter (drywall filter) works well for cleaning in/around the stove itself. Depending on the ash content, most of the time, once or twice a season should be enough, I normally just clean mine out at the end of the season when I shut the stove(s) down. It has 1/4-1/2" of ash in the pipe, but not enough to block the draft or anything. You will get the ash chunks and fines both in your ash pan, sometimes some unburnt coal too. Nothing you can do about it, some brands burn better than others, some produce more ash then others too.
Cleaning the ash grate is the same, you will have to shut it down and vacuum it out, maybe use a piece of wire/coat hanger to poke the holes clean if needed. Sometimes the grates are removable and should be cleaned out under them too. Some stoves you can remove the combustion blower from teh back to access under the grate area.
AS for the control, the combustion blower may run 24/7 and if yours only has a rehostat for feed rate, then it will run constantly. Not sure how the thermostat is hooked up, but normally it would control the on/off cycle of the stoker when it call for heat or not. My keystoker does this, you can hear the relay click on the back of the stove when the thermostat calls for heat.
I run my stoves mostly 24/7 from Nov thru April. A quick vaccum maybe once a week or so the best I can and they seem to run fine. But a good tear apart, clean, lube,etc in the spring is always recommended.
You may look at the CoalTrol Control System, that will regulate the coal stoker and combustion blowers for optimum heat transfer.
I have the coaltrol on my Hyfire and it works great and maintains almost a perfect set temp.