Learn English – Difference between ‘sympathy for’ and ‘sympathy at’

To the extent that there is a difference I would say that "make a case" suggests something particularly compelling about your argument, while "present a case" is more of an objective description of what you will do.

In your first example there is an implication that the reader should re-examine the assassination. If "makes" were replaced with "presents" I would not perceive any such implication and would instead interpret the statement as an invitation for me to review the argumentation and come to a conclusion, whatever that conclusion may be.

This is a pretty informal sentiment on my part though. "Present a case" feels more formal to me and is not an expression that I come across very often. "Make a case" is extremely common. However, I may be responding to my sense of their relative usage frequency rather than a real usage difference. Regardless, I don't think that you would cause any confusion at all using either phrase in any situation, or that a listener/reader would draw a substantively different meaning from one or the other.

The most common preposition used with "prices" is "of", but "for" is sometimes used as this ngram shows.

I would suggest that "prices for" is only really appropriate if there is some human element, because the word carries purpose or belonging. For example:

The shopkeeper is introducing new prices for his customers.

To me, "for" does not sound correct in your example, and that is probably because there is no person involved. I would definitely express it as:

Prices of gasoline have been fluctuating all month.

You may also note that the ngram above shows much less frequent use for the plural of "price". That is because it is more common to speak of one price because multiple identical items have the same price. However in your example it may well be correct to use the plural because the same fuel is often offered at different prices in different places, so when speaking blanketly about fuel costs over the country it seems correct to say "prices".