Some. I actually cancelled my subscription with them because of the horrendously large Google Home ads on all the paid crosswords. When I asked them about it I got about four non-answers — it's ridiculous that even if you pay they still serve you ads.

Newspapers have always included ads even if you pay; not sure why anyone would expect “on the internet” to change that.

Because I pay specifically for only the crossword part. I bought a book of 50 (of NYT puzzles) for the same price, and it came with no ads. Much better deal, if you ask me.