(a) The order of the court approving the improvement plan as provided in § 14-125-602 or the final improvement plan as provided in § 14-125-603, and establishing the improvement project area described therein, shall have all the force and effect of a judgment.
(b) Any landowner within the project area may appeal from the order within thirty (30) days after it has been made, but if no appeal is taken within that time, the order shall be deemed conclusive and binding upon all the land within the boundaries of the project area, and upon the landowners.
(c) Any owner of land within a proposed project area may within like time appeal from any order refusing to approve a proposed plan and establish a project area.