We are about to buy an apartment with 30 year old oak parquet in fair condition. We would like a quieter, less busy look than the parquet. Can parquet be stained very dark brown to make it look more subtle?

Yes, parquet is often stained. If your's is oak, then there's no prblem staining it. You'll need to find an experienced flooring contractor who is an expert at refinishing. Parquet needs to sanded slightly differently than plank or strip floors. There are also tricks to getting the color you want; like "popping the grain" to get the stain to absorb better after screening. I've come across a few maple parquets that didn't stain dark as well as oak but I was still able to stain them and they looked ok. By going dark, you will obscure the grain of the flooring and therefore obtain a more monochromatic appeareance in the floor. Good luck!