Yes, I have been doing this since the beginning.
When starting the machine for the first time (new machine) and after each descaling process, you have to confirm that you have not inserted an Aqua Clean filter. This question comes up the first few times (approx. 5x?) and then the machine no longer asks.

Yes, that will be fine.
We also have a softening system, but we use the filter anyway. The machine was expensive enough ;-)

Yes. Since I have a softening system, I also use the machine without a filter.