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I believe the first one is from PT 54, Here they are;

PT 54(?) LR S1 Q19:
Even those who believe that the are of each age and culture has its own standards of beauty must admit that some painters are simply superior to others in the execution of their artistic visions. But this superiority must be measured in light of the artist's purposes, since the high merits, for example, of Jose Rey Toledo's work and his extraordinary artistic skills are not in doubt, despite the fact that his paintings do not literally resemble what they represent.
[Stem] The claim that some painters are superior to others in the execution of their artistic visions plays which one of the following roles in the argument.
c) It is a claim that, according to the argument, is to be understood in a manner specified by the conclusion
d) It is a claim that the argument derives from another claim and that it uses to support its conclusion
For Q19 I chose "d" but the credited response was "c". Please, please, please help me explain why "c" is the credited response and "d" isn't.

PT 53 LR S3 Q11:
A recent epidemiological study found that businesspeople who travel internationally on business are much more likely to suffer from chronic insomnia than are business people who do not travel on business. International travelers experiences the stresses of dramatic changes in climate, frequent disruption of daily routines, and immersion in cultures other than their own, stresses not commonly felt by those who do not travel. Thus, it is likely that these stresses cause the insomnia.
[Stem] Which one of the following would, if true, most strengthen the reasoning above?
c) Businesspeople who already suffer from chronic insomnia are no more likely than businesspeople who do not to accept assignments from their employers that require international travel.
e) Some businesspeople who once traveled internationally but no longer do so complain of various sleep-related ailments
I really didn't like "e" but out of the five is was the one I least disliked.

IBTL

The conclusion of the first article is that The superiority of execution is to be understood as "execution of the artist's intent" rather than some objective representation. That is the correct answer as well - "Some painters are superior to others" is mean to be understood as "in execution of their intent".

The second article is obvious. It confuses correlation with causation. Are businesspeople suffering from insomnia as a result of their travel, or are they traveling because they suffer from insomnia? In order to specifically prove via this correlation that travel causes insomnia, you have to assume that it isn't the opposite - insomnia causing travel.

Second question first, since it's a bit easier:

The argument is that travel causes insomnia. Answer C strengthens that argument more, because it speaks to the fact that there is not just a higher amount of people who already have insomnia accepting traveling positions. Therefore, C tries to do away with a possible correlation != causation argument, and strengthens it more than D, which simply says people who once traveled might still have insomnia (in other words, D doesn't even speak to the argument, so it can't strengthen it.)

For the first question, you have to pick apart the parts of the statements:

1: Each era has different ideas of beauty
2: Some artists are technically superior, no matter what the era's idea of beauty is.
3: This superiority must be measured not by the era's idea of beauty, but by what the artist is trying to accomplish
4: Jose Toledo is regarded as a superior painter, even though his paintings don't look like what they represent (i.e. Toledo is a skilled painter, but does not paint so that people understand his work)

So, with answer D, part 2 would have to come from 1, 3, or 4, but it doesn't. Part 2 stands as an assertion by itself. In Answer C, though, Part 4 is used to shed light on exactly what the statement means by Part 2. In other words, Part 2 is made more clear once we read Part 4.

(That, of course, is my take on both these questions. I haven't studied for the LSAT in a long, long time though, so I'm a bit rusty, and don't know the TLS lingo for explaining these!)