It is suitable for parquet. Regarding the use of third-party products, here is what the brand states on its website:

"Yes, you can use another product of your choice with Crosswave. However, it is strictly forbidden to use household vinegar, or any other acidic product, which will lead to corrosion of your appliance. This will invalidate the warranty of your appliance. Also, the use of products that generate foam is not recommended. Finally, you will probably need to do several tests to find the ideal dosage that leaves no traces. The advantage of Bissell cleaning products is that they have been developed specifically for use with your CrossWave and are perfectly dosed for it."