(1)

Option (e) Based on Opportunity Cost Theory

This can be explained below :-

Option (a) is wrong because it is an assumption of the Comparative Advantage Theory. It says that transportation, insurance, etc. costs are zero. Yes, there involves no transportation costs and insurance costs etc in carrying out the trade between the two countries that are taken in this theory because these are the services are inevitably required during trade between the two countries, hence their cost is considered to be zero.

Option (b) is wrong because it is an assumption of the Comparative Advantage Theory. It says that workforce is homogenous. Yes, all the labour units taken to produce the given two commodities are taken homogenous.

Option (c) is wrong because it is an assumption of the Comparative Advantage Theory. It says that perfect competition conditions apply. The theory assumes that there is perfect mobility of factors without any diminishing returns. So, yes perfect competition conditions apply.

Option (d) is wrong because it is an assumption of the Comparative Advantage Theory. It says that fixed cost applies in production. The theory assumes that fixed proportion of labour is used in the production of all the commodities. Therefore, the theory is based on the assumption of constant costs or say fixed costs.

Now, Option (e) is right because it is not an assumption of the Comparative Advantage Theory. It says that the theory is based on the opportunity cost theory.
No, opportunity cost theory is not the base of the Theory of Comparative Advantage.

Opportunity cost theory says that if a country can produce two goods say A and B then the opportunity cost of producing A will be the amount of B that is given up in order to produce one additional unit of good A whereas Comparative Advantage  theory states that if a country specialises in producing goods where they have a lower opportunity cost then there will increase their economic welfare.

Therefore, Opportunity Cost theory isn't the base of the Comparative Advantage Theory. Hence, this isn't the assumption which makes this option the correct answer of the given question.
 

(2)

(d) There is different satisfaction at every point on the
curve.

This can be explained below :-

Option (a) is wrong because it is a property of indifference curve. It says that equivalent satisfaction is involved at every point on the curve. So, yes indifference curve itself shows the different bundles of two commodities that are consumed in such a way without changing the level of satisfaction. So, taking any point on the indifference curve gives us the equal level of satisfaction.

Option (b) is wrong because it is a property of indifference curve. It says that indifference curve are convex to the origin. Yes, they are convex to the origin because this is based on the assumption of marginal rate of substitution which says that in order to increase the consumption of one good, the other good has to be given up. So, according to the assumption of marginal rate of substitution indifference curve is convex to the origin.

Option (c) is wrong because it is a property of indifference curve. It says that farther is the indifference curve from the origin, the higher is the prediction level.
Now, higher indifference curve gives higher level of satisfaction because it involves higher quantity of one good or of both the goods.

Option (e) is wrong because it is also a property of indifference curve. It says that indifference curves never cut each other. Yes, they two curves never cut each other because each curve shows a different level of satisfaction and due to this it will be invalid if two curves will cut each other because then the level of satisfaction of two curves will be equal at that point and that's not possible. Hence, two indifference curves never cut each other based on the fact that two indifference curves show different level of satisfaction.

Now, option (d) is right because it is not a property of indifference curve. It says that there is different satisfaction at every point on the curve. This is a not a property of an indifference curve.
Taking any point on the indifference curve gives equal level of satisfaction. This is because indifference curve itself is based on the fact that indifference curve shows different bundles of two commodities in such a way without changing the level of satisfaction.
Hence, all the points on the indifference curve shows same level of satisfaction.