Not if they are only using it to route the DNS traffic (though in that case a cheaper VPS might be better), which will work if the ISP is only poisoning DNS replies and not (which is often the case) blocking traffic to the target servers entirely.

The problem with this is you are adding a moving part to your DNS lookups. It might be worth adding two on separate VPS hosts and have your resolver fall back to the second if the first goes down.

Another, usually more minor, problem is that some services (like CDNs) use the source of your DNS query to modify the response so you get sent to a topologically near-by end-point. This means you might notice such services being slower as you are sent to a PoP near your VPN host not one closer to your actual location.

Not for DNS lookups. Hetzner forwards complaints from copyright holders, they don't proactively snoop traffic to make sure you don't access 1337x at all. It's legal to access the site.

Oh well OP was doing shady stuff ... then yeah they should continue with using VPN provider. VPN providers are shady AF, I don't think there is VPN provider I would trust more than my local internet provider.