Let's not get distracted away from the real idea here. Cold war refers to the use of threats and intimidation to gain or hold control. Hot wars include physical violence and blood shed. The Cold War definitely had global implications.
Those conflicts that rose to the point of actual war and loss of life were no longer "Cold War's", they may have been a result of what was going on within the Cold War. The Cold War was typically thought of as the disagreements between the Soviet Union and the United States and did not result in actual fighting.
Sure, I'll play devil's advocate. There was little similarity between how the Cold War played out in Europe--an armed standoff for 43 years--and how it played out in Asia, with two long, bloody wars and a series of brutal and even genocidal civil wars. There is also little similarity between either of those and what the Cold War in Africa looked like, which centered more around foreign aid and bloody coups than large scale war or alliances. Latin America, again, something else different altogether, as our goal was to keep friendly governments in place, even if they were dictatorships, and the use of economic blockade in the case of Cuba (not to mention guerrilla invasion) is pretty rare in the Cold War.
I have to agree with #2 on this one. When we think of the Cold War, we cannot get away from the fact that essentially it was a long running conflict played out between two sides. The location and actual manifestation of each "side" was different in each uprising, but to treat the series of "wars" as isolated incidents would be to completely ignore the long-running conflict and the wider context against which such "mini-wars" were played.
No, I do not agree with this statement. It is, of course, true that the Cold War played out across many different regions. It is also true that the conflicts in the different regions were somewhat different from one another. However, they were all part of the same general conflict and this similarity was more important than the differences.
The major point here is that all of the regional conflicts played out in similar ways because they were part of the broader overall conflict. In all cases, the superpowers tried to use the smaller countries and movements as proxies in their overall conflict. In addition, success by one side in one area could affect the overall strategies of both sides. If, for example, one side lost a conflict in Asia it might feel that another conflict in the Middle East was more important.
In these ways, the various regional conflicts were tied together in ways that were much more important than their differences.