How to clean removr and clean this vent

Somewhere in that set-up there should be a slip (adjustable) section of connector. If not, when you disconnect the connector at the ceiling support box, the top sections will probably drop down. You just have to make sure that you have removed any screws from the flue collar on the stove so that the bottom piece doesn't get damaged. I'd suggest you don't do this alone as it's gonna be kinda awkward...

Three burns is much too soon. I would clean it after you have burned through the first half cord of wood. That will give you an approximation of how frequently it will need cleaning. If there is very little accumulation and it's powdery, then wait until you have burned a full cord before the next cleaning. If you find lots of black shiny flakes then keep cleaning every half cord.

The interval between cleanings is going to depend on the wood, the flue and the operator. You'll get a feel for this as the season progresses. If the wood is nice and dry and the stove is run well and the flue is mostly interior, you should be able to go a full season between cleanings.