'assess' In general it means to regard a situation, a person or any matter in order to judge it in rational manner. In this sense it is very much a synonym of 'evalute'. It means in particular also to calculate the the worth or cost of something. "to assess the value of the property." So the subject of assessment could be a problem, situation ,an amount or value. "evaluAte" Very much the same as 'assess' in its general meaning. It is when one thinks carefully before one judges, assesses and determines the worth or value of something. "estimate" does have a slightly different meaning. It refers to determining and suggesting the value, worth or amount of something,you are dealing here with accurate amounts and numbers and not with problems or situations. Usually tangible present information is used to guess this amount or value . " The total cost was estimated at X dollars." ( Here it is a definite amount (number) calculated probably depending on existing information.)

You need to pay far more attention to what is a verb and what is a noun!