This is a core word more than a sprawling family. אֶרֶץ means land, earth, country, one of the first words a learner meets, and in Israel often just haAretz, "the Land". From it grows one adjective, אַרְצִי: belonging to the land, hence worldly and down-to-earth, and also national, of the whole country. So the root gives you both a place and a way of being rooted in it. Every word below is verified against pealim, niqqud included.
No verb is lexicalized on this root; it is a noun root, anchoring a place rather than an action. That is common for the oldest, most concrete words: they name a thing the language is built around, not a deed.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.