This site produces no cookies of its own, the sole cookies created are part of Cloudflare's proxy product and are necessary for it's normal operation (apparently). I can't turn those off, but you can, from your browser, as was intended - I won't be upset, though you'll probably have to pass a bot captcha every couple of pages.
You can read a bit more about Cloudflare's GDPR stuff if you want more information, I guess.
Absolutely no information is deliberately collected by this website.
Cloudflare and myself will collect IP addresses, user agents, referers, and timestamps as part of the normal operation of a server. I cannot speak for Cloudflare, but mine are disposed of after 7 days for normal web logs. Attacks and others are kept longer.
The search feature is provided by Google, who will have their own set of creepy policies - if you're at all concerned about privacy you probably don't want to use that feature.