Yes, but the adverb usually comes before the verb. So здесь жить is simply to live here. It could answer the question, "What do you think about this city?" But saying жить здесь means that you're stressing where you enjoy living. It could answer the question, "From this list of cities, where do you like living?"
90% of the time you will use the singular or plural third person of the verb (нравится и нравятся). The thing that is liked is in nominative, and the person who likes it is in dative case.
You would only use another conjugation, like нравлюсь, to talk about how someone else likes you (Ей не нравлюсь would be "She doesn't like me", not "I don't like her").
It's like "me gusta" in Spanish or "mir gefällt" in German.
I would say it's even more like "Living here is liked to me" since the "me" is in dative case and not instrumental.
Wiktionary offers "To please" as a second translation, which might even make it easier to remember - "Living here pleases me" (except that sounds a little foreign in English).
The -ся is a reflexive particle, it makes the verb intransitive. In simpler terms, it means the thing being liked is going to be in the nominative case and the verb is conjugated based on that thing, and the person or thing doing the liking will be in dative case.
Here you have a verb infinitive (жить) that is being liked. That gets treated like a single third person entity (like "it"), so the verb нравиться is declined accordingly.
You most often see it in the third person singular or plural (нравятся), though you can use it when talking to a person, too (ты мне нравишься).
I hope that clears things up, if not please ask more questions.