Praise be to Allah.
If a man divorces his wife with one talaaq, it is permissible for him to take her back so long as she is still within the ‘iddah period. Taking her back may be done verbally, or by having intercourse with her with the intention of taking her back. If the ‘iddah has ended, he cannot take her back except with a new marriage contract.
He may also marry a second wife before divorcing the first one or afterwards or during the ‘iddah, because there is no connection between the two matters. And he does not have to tell the first wife or get her agreement, because Allah has permitted the man to have four wives on condition that he treat them fairly. Allah, may He be exalted, says (interpretation of the meaning): “then marry (other) women of your choice, two or three, or four; but if you fear that you shall not be able to deal justly (with them), then only one” [al-Nisa’ 4:3].
A misyaar marriage, if it fulfils the conditions of marriage, namely the consent of the woman, the presence of her guardian and two witnesses, and the mahr, is a valid marriage and there is nothing wrong with a woman yielding some of her rights to accommodation, a share of her husband’s time or maintenance.
But marriage without the guardian is not valid, because the Prophet (blessings and peace of Allah be upon him) said: “There is no marriage except with a guardian.” Narrated by Abu Dawood (2085), al-Tirmidhi (1101) and Ibn Maajah (1881) from the hadeeth of Abu Moosa al-Ash‘ari; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
And the Prophet (blessings and peace of Allah be upon him) said: “There is no marriage except with a guardian and two witnesses of good character.” Narrated by al-Bayhaqi from the hadeeth of ‘Imraan and ‘Aa’ishah; classed as saheeh by al-Albaani in Saheeh al-Jaami‘, no. 7557.
And he (blessings and peace of Allah be upon him) said: “Any woman who gets married without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid.” Narrated by Ahmad (24417), Abu Dawood (2083) and al-Tirmidhi (1102); classed as saheeh by al-Albaani in Saheeh al-Jaami‘, no. 2709.
It is not permissible to conceal the matter from her guardian and the marriage is not valid unless it is done by the guardian himself or the guardian delegates someone to do the marriage contract on his behalf.
It is not permissible for the imam to take his place unless the guardian has delegated him to do the marriage contract.
The condition of the guardian being present is emphatically stipulated in the case of misyaar marriage, so as to differentiate between it and immoral relationships.
See also the answer to question no. 82390.
And Allah knows best.