(a) The commissioners shall thereupon appoint an assessor to assess the benefits which will accrue to the real property within the district from the making of the improvement and the damages which will be caused thereby. The assessor shall take an oath that he will well and truly assess all benefits that will accrue to the landowners of the district by the making of the proposed improvement.

(b) He shall thereupon proceed to assess the lands within the district, and shall inscribe in a book each lot, block, and tract of land within the district. He shall put opposite each tract the assessment of the benefits and damages which will accrue to the lots, blocks, and tracts of land by reason of the improvement.

(c) His assessment shall embrace not merely the lands, but all railroads, tramroads, telegraph, telephone, and pipelines and other improvements on real property that will be benefited by the making of the improvement.

(d) The assessor shall place opposite each tract the name of the supposed owner as shown by the last county assessment. However, a mistake in the name shall not vitiate the assessment, and the assessor may correct errors which occur in the county assessment list.

(e) The assessor shall also assess all damages that will accrue to any landowner by reason of the proposed improvement, including all injury to lands taken or damaged. Where the assessor returns no such damages as to any tract or parcel of land, it shall be deemed a finding by him that no damages will be sustained.

(f) When the board shall make the levy of taxes, it shall be the duty of the assessor to extend the amount levied and set the amount opposite each benefit assessed in a column marked "Annual Collection."

(g) The assessor shall hold his office at the pleasure of the board, which can fill any vacancy in the position of assessor.