You installed dillo but didn't set the extension to load at start-up, so you need to do "tce-load -i dillo" before it will run again. Installing programs "ondemand" might be better for your usage using "tce-load -wo", or use the GUI as is described the book (which I can't believe you really read).
I find Firefox runs OK with 2GB RAM, but after tweaking lots of settings to optimise it. 1GB might still be tight. YouTube isn't going to happen - it needs much more. Try front-end websites like Invidious or GenYT to download video files you can watch with a video player program like VLC.
Dillo doesn't support Javascript, which Google requires now as well as YouTube. Still, I use it for most of my web browsing. You can click on the manifying glass icon next to the URL bar to open the search window where you can enter a search query which is loaded from Duck Duck Go.
Unfortunately the Tiny Core forum webmaster has turned off using the PHPSESSID string so you need to enable cookies in Dillo which are disabled by default. You do this by creating a file containing "forum.tinycorelinux.net ACCEPT_SESSION" at "~/.dillo/cookiesrc". That's sure to give you horrors though, so yes pick another web browser. I suggested Seamonkey before since it's closest to the capabilities of Firefox, though I don't use it myself. Netsurf might be better for performance while still being a bit more user-friendly than Dillo.
Repeat: Playing YouTube videos on the main YouTube website isn't going to work well or at all on your PC unless you download them using another website (or yt-dlp in the terminal, but I guess you won't like that). If that's what you want it for then I'd give up now. Libreoffice might be the same, I use Ted but I don't think you'll like that, Abiword might be a better option.