Go to about:profiles. From there, you can create and switch between profiles. This is not as convenient as it perhaps should be, but I did find one add-on that claims to simplify the process [1].
I'll suggest Searx/SearXNG as a search engine. It's self-hosted, but you can find public instances at https://searx.space/
If you decide to go the self-hosted route, it's trivial to deploy with searx(ng)-docker. Being a meta-search engine, it can pull results from Google, Bing, DuckDuckGo, dictionaries, torrent sites, etc; this gives it a degree of customisability that traditional search engines don't have.
I'll also mention Whoogle, which serves as a libre front-end to Google, although it doesn't currently support any other search engines.
Go to about:profiles. From there, you can create and switch between profiles. This is not as convenient as it perhaps should be, but I did find one add-on that claims to simplify the process [1].
[1] https://github.com/null-dev/firefox-profile-switcher