OK I’ve had a read back through the first post, let me have a go at my understanding of LDS eternal marriage etc.
Firstly, the poster you quoted was referring to exaltation when he said “,eternal life”. Marriage is not required for Salvation but it is required for Exaltation.
Three degrees of glory are Celestial, Terrestial, Telestial, the Celestial being the highest and it is also in 3 “parts”. It’s the highest part of the celestial kingdom that requires marriage. I believe the degrees of glory comes from a Bible passage which talks about the sun, the moon and the stars (I’ll try looking it up!)
A couple may be married civilly (ie in the LDS chapels or elsewhere) and this is for time only. The marriage ends at death.
A couple who are considered worthy LDS may marry in the temple (for time and eternity)
A man may be sealed to more than one woman but a woman can’t be sealed to more than one man. So if a man’s wife does, he may remarry for time and eternity (assuming the woman he marries wasn’t sealed before although she could choose to cancel this sealing and be sealed to her second husband instead)
Currently all people who have died are in spirit prison or spirit paradise. Noone has entered heaven, that comes after final judgement. Marriage can be performed in this life or by proxy (along with baptisms, sealings, endowments etc) for the dead in Spirit prison/paradise and through the millennium but these will stop once Final Judgement is here ie no marriages are performed in Heaven.
Therefore people are given every opportunity in this life and the next to receive the ordinances they require to enter the highest degree of the highest glory (celestial kingdom). I’m not sure what the poster was talking about when he said those who don’t have a temple marriage don’t attain eternal life. I can only assume he means at final judgement those who still reject Christ, and all the ordinances needed for Exaltation, won’t receive them and therefore won’t be able to enter the highest degree of the highest glory. They still have free will in the Spirit World.
Women are not assigned men…at least I haven’t found any documented evidence for this or was ever taught it when I was LDS.
The bit I am unsure on is I believe they only seal by proxy those who were married in this life therefore I’m not sure how people who die unmarried still get tbe opportunities.
Hope that helps (and hopefully Jane will correct me if I have made mistakes!)