(1) tournaments, challenges, friendly matches are all played at tournament card levels which are quite easy to reach as f2p (and friendly and special challenges level new players up to the tournament levels).
(2) in 2v2, by far the most fun game mode for me, card levels are massively less important since there's no ladder.
(3) the 1v1 ladder is not a pure skill matchup but still finds everyone a range where they have essentially a 50% win rate based on a combination of progress and skill.
(4) yes the top of the ladder players have almost all spent a lot of money but most of the playerbase of any game isn't serious about being on the very top of the leaderboard. A smaller factor is that the most talented f2p players are sponsored with max decks and stop grinding f2p challenges.