I don’t know that you can do it without an extension, however Mozilla has put out an extension called “Firefox Translations” that translates webpages locally on your computer with a downloaded dictionary. So far it works well in my experience, though I don’t know any other languages, so I can’t really speak to its accuracy. That being said, so far I haven’t come across any nonsensical translations.

You can try, but it probably won’t be as good in terms of translation quality and languages covered, at least yet, you can already get a taste by installing the Firefox Translations extension.
If you make heavy use of website translations then you’ll probably have to keep it, otherwise you’ll probably get by with the integrated translations and, when that’s not enough, just paste the URL into Google Translate to get that one-off translation

Not familiar with the extension you mentioned, but you can refer to the screenshots in this article to see how you’d access the new translation feature.

Note that it’s based on Bergamot, which is the same engine used by the TranslateLocally extension. I’d expect these two to produce comparable translations, but I have no idea how they compare to TWP. You’d have to try it and find out.