Using dictionary.reference.com:
Excursion - a short trip or outing to some place, usually for a special purpose and with the intention of a prompt return
Trip - 1. a journey or voyage: to win a trip to Paris. 2. a journey, voyage, or run made by a boat, train, bus, or the like, between two points: It's a short trip from Baltimore to Philadelphia.
Hence where "excursion" is used for an outing, "trip" is also an acceptable word.
For "trip" definition 1, "excursion" could also be used, provided the trip is short enough. Although it's not explicitly stated in the definitions, I'd suggest that if it is up to a day long then it can be either a trip or an excursion, but if it is longer then it would be a trip. For example, a 3 day visit to Paris might be a trip, but a day's outing to see the Palace of Versailles could be described as either a trip or an excursion.
For "trip" definition 2, "excursion" would not be a valid alternative word. i.e. where you are only talking about the journey in terms of transport, and not in terms of actually "doing anything" at the destination, then "excursion" is not valid.
As noted by @Mrstupid in comments, "trip" is more commonly used than "excursion" in India; in my experience this is true in the UK too; and in JR's experience it is true in the US.
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.
Best Answer
"Case" here means "arguments, facts, and reasons in support of or against something". The case for [exploring] Mars consists of arguments, facts, reasons, etc in support of that activity.
die Argumente für/gegen might be an equivalent in German, although that is off-topic.
Case