Not a specific site, but you can get the old internet feel using Tor Browser and exploring Tor websites. Last time I checked it out it felt like going back to the early 2000s or late 90s depending on the website. There are also some sites hosted on IPFS that looks like something from Geocities.
Unfortunately no. It’s been a few years since I’ve taken a look at it. But it shouldn’t be too hard to find Onion sites that list other sites. And there are Onion search engines out there as well. Maybe you could start here.