Learn Dutch: De buurt is tamelijk levendig. - The neighborhood is fairly lively.

They are all adverbs of moderate degree, but they have slight differences. Tamelijk means "fairly" or "quite" and is very neutral. Vrij is similar but can feel a bit more positive. Nogal translates to "rather" or "quite a bit" and often implies that the degree is more than expected, sometimes carrying a slightly negative tone.

Could I use best in this sentence instead of tamelijk?

Yes, you could say De buurt is best levendig. When used right before an adjective, best doesn't mean "the best"—it translates to "pretty" or "quite". Saying best levendig often implies a slightly subjective or pleasantly surprised opinion, whereas tamelijk just states a neutral fact.

The word levendig looks like it comes from leven (to live). Is that right?

Exactly! It comes from the noun or verb leven (life / to live). The suffix -ig is frequently added to Dutch words to turn them into adjectives, much like "-y" or "-ly" in English. The -d- in the middle connects them, creating levendig (lively).

How should I pronounce the ending of tamelijk?

Remember that the common suffix -lijk is never pronounced the way it looks. The ij sounds like a short, unstressed "uh" (a schwa), so the entire ending sounds like "luk".