Hi!
The DIY book contains the following text, roughly translated:
- Disassemble the control valve with the attached pipes at the top (for venting).
-To drain the water, loosen the screw under the filter and allow approximately 100ml of liquid to drain out...
-Always replace the O-rings when installing a control valve.
...is of course special waste, what you are disposing of. So, don't just pour it into the nearest drain

.
Your concerns about air are relatively unfounded, as the tandem pump also has an "air separator" for positive displacement pumps, so the elements are not affected by it.
Best regards,
dirk