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Q. Were there other people in Israel that didn’t have Israel descent at the time?
Yes. While there were always foreigners in Israel, the foreigners at this point of time included those whom Shalmaneser, the king of Assyria, settled in Israel.
Quoting from NASB,
2 Kings 17:24 The king of Assyria brought men from Babylon and from Cuthah and from Avva and from Hamath and Sephar-vaim, and settled them in the cities of Samaria in place of the sons of Israel. So they possessed Samaria and lived in its cities.
Q. And did they build the wall as well?
No. Nehemiah made it clear that foreigners (among whom were Sanballat the Horonite and Tobiah the Ammonite official, and Geshem the Arab) would not have any part in it.
Quoting from NASB,
Nehemiah 2:20 So I answered them and said to them, "The God of heaven will give us success; therefore we His servants will arise and build, but you have no portion, right or memorial in Jerusalem."
Q. Did they worship the same God?
They did not worship the God of Israel. They continued their earlier practices of worship. See 2 Kings 17:30-32. They did seem to fear the LORD, the God of Israel. But they continued to serve their own gods.
Quoting from NASB,
2 Kings 17:33 They feared the LORD and served their own gods according to the custom of the nations from among whom they had been carried away into exile.