https://addons.mozilla.org/en-US/firefox/addon/toby-for-tabs/

I expect you have tried to search for it in Firefox, but have you tried sideloading it somehow?

As far as I know Firefox supports a superset of the APIs that Chrome support, so it should be a possible?

While there might not be an addon that perfectly emulates every feature of Toby on Firefox, I am fully confident you can achieve all of its features with settings, config/userchrome edits, or some of the addons that are available. Personally I use Tab Session Manager and Tab Center Reborn (heavily edited though), so you might look into those and see if they have features you like.

You can do that in firefox. Add the search engine, go to settings > search and add a keyword in the list

I use duckduckgo and they have bangs. Put !yt at the start of your search and it'll automatically search youtube, !g for google, !a for Amazon, etc... Loads of bangs for basically every service out there.