These were devout believers trying to do their best to not lie while living a very difficult practice they believed God had commanded.

Technically the denials, whether to Emma or other listeners, were truthful if they referred to legal polygamy, Islamic polygamy, or John C. Bennett's "spiritual wifery."

Accusations that Joseph Smith lied to Emma are based upon assumption. There is no evidence to support this and Emma continued to believe in Joseph as a true prophet throughout his lifetime.

Joseph Smith’s plural marriages did not break the anti-bigamy laws of Illinois. It is debatable whether his secret plural unions could have been prosecuted as "open adultery," although it is certain that Illinois courts would not have recognized the marriages as valid.

Joseph could truthfully deny practicing legal polygamy or polygamy as practiced in Islam. Some pluralists even went so far as to say celestial marriage was distinct from "polygamy" as generally termed in that era.

Joseph used careful language when publicly discussing plural marriage. Later historians would report the verbiage as "verbal gymnastics" and circumlocutions. It is plain that the Prophet and other participants in plural marriage were trying to not bear a false witness.

Scriptural examples exist where deception was permitted or required in order to serve God’s purposes. Abraham introduced his wife Sarah as his “sister” to King Abimelech, not disclosing she was his wife (Genesis 20:1-7), a tactic he had implemented earlier in Egypt:

And it came to pass when I was come near to enter into Egypt, the Lord said unto me: Behold, Sarai, thy wife, is a very fair woman to look upon; Therefore it shall come to pass, when the Egyptians shall see her, they will say--She is his wife; and they will kill you, but they will save her alive; therefore see that ye do on this wise: Let her say unto the Egyptians, she is thy sister, and thy soul shall live. And it came to pass that I, Abraham, told Sarai, my wife, all that the Lord had said unto me--Therefore say unto them, I pray thee, thou art my sister, that it may be well with me for thy sake, and my soul shall live because of thee. (Abr. 2:22-25; see also Genesis 12:10-20.)

The destruction of the Nauvoo Expositor was ordered by the Nauvoo City Council and carried out by them.

The 1835 Doctrine and Covenants section CI verse 4 specifies: “we believe that one man should have one wife, and one woman but one husband.” However, it does not say only one wife. It is ambiguous regarding the Church’s stand on polygamy.

Additional Resources:

“Thou Shalt not Lie” and Denials of Polygamy

Joseph Smith’s Pre-Nauvoo Reputation

M. Scott Bradshaw, “Defining Adultery under Illinois and Nauvoo Law,” in Sustaining the Law: Joseph Smith’s Legal Encounters, eds. Gordon A. Madsen, Jeffrey N. Walker, and John W. Welch (Provo, Utah: BYU Studies, 2014), 401–26.