Is it permissible to buy a plot of land and pay part of its price, then sell portions of it to others before fully acquiring it, and agree with the landowner to postpone the payment of the remaining amount?

The sale between you and the landowner has not yet been completed, and therefore the ownership of the land remains with its owner. It is not permissible for a person to sell what he does not own, due to the saying of the Messenger of Allah, peace and blessings be upon him: "It is not permissible to combine a sale and a loan, nor two conditions in one sale, nor to sell what you do not possess," and his saying: "Do not sell what is not with you."

Therefore, it is not permissible for you to sell this land until you have purchased and taken possession of it, due to the saying of the Messenger of Allah, peace and blessings be upon him: "Whoever buys food should not sell it until he has taken possession of it," and his prohibition, peace and blessings be upon him, against selling goods where they are bought until merchants take them to their homes.

A condition for the validity of a sale contract is that the price must be known and specified. If this person sells to you without specifying the land's price, then the sale is not valid, as a condition for validity is knowledge of the sold item and its price.