Is the second marriage of the questioner valid, given her fear that she is still the wife of the first man, especially after he divorced her, then took her back by merely saying: "the words of رجوع (taking back the wife)," and she did not explicitly agree, and he spoke to her words specific to married couples, then sent her the deferred dowry?

The right of رجعة (revocation of divorce) belongs to the husband, and the wife's consent is not a prerequisite for it. If the husband pronounces رجعة during the 'iddah (definition) (waiting period), the woman remains under his marital authority.

Therefore, her marriage to another man is considered invalid because she is still under the marital authority of her first husband. This second marriage must be annulled.