First, since you mentioned "Americans and the rest of the 
    world", does the same trend hold for the people on the other 
    side of these conflicts?

Yeah and no. It's so hard to measure the human cost of war because so many of the deaths are indirect.

Operation Rolling Thunder (50 years ago) was probably the last time the US took mass numbers of lives directly, with the high end of estimates approaching something like an average of 5,000/month.

Estimates of deaths from the Iraq War range from 150K "violent deaths" to 1mil "excess deaths" which would include all sorts of indirect causes: https://en.wikipedia.org/wiki/Casualties_of_the_Iraq_War

Those are horrific levels of loss but nowhere near the toll of WWII.

    Second, the number of people who fought in each of these    
    wars is also pretty different. Isn't a more direct 
    comparison something more like "deaths per combatant per 
    month" rather than "deaths per month"? 

It depends. Do we want to measure how risky it is to be a combatant, or how risky it is to be a human being on Earth?

If it's the former, then "deaths per combatant per month" is what we want. That would be interesting, though I question how broadly useful it would be. It would obviously be directly useful for combatants (or those considering becoming combatants) but is probably not useful as an overall indicator of "hey, how's the human race doing in general?"

If it's the latter, the stat we probably want is "war-related deaths per human being per month" or something like that. That would be a good indicator of overall levels of war and strife. It would take into account the increased population of the world as well.

Even if (heaven forbid) we had a conflict that results in WWII-like absolute levels of deaths today, that would represent a far lower number of deaths as a percentage of the human population lost.

On the first question, there is some scholarly debate, but as far as I can tell as an outsider the general consensus is that there are fewer deaths due to armed conflict than anytime in the last two millennia. Even something as terrible as the Syrian Civil War (~half a million dead over a decade) is the sort of civil unrest that was happening at multiple places across the world during the 17th century (see _Global Crisis_ by Geoffrey Parker for how horrible the 17th century was, all around the world). It's just the numbers are a lot less precise than we have for American deaths in military operations, so there is a lot more room for debate. This can be complicated even for something well documented and recent like World War Two: do you count the Bengal famine as part of the war dead? It killed ~2 million Indians, but not directly due to the war, it's just that the ships that in peacetime would have been carrying food to India to relieve the famine were instead carrying weapons (and food) from the US to Britain. Did they die due to the war? Or due to British colonialism and evil Winston Churchill? Well, a whole lot of the deaths in 17th century wars were due to war-related famine and disease, so if you don't count the Bengal Famine but do use the higher numbers for the 30 Years War it isn't a clean comparison, etc.

On the second question it's even harder to say. Would probably be a masters degree level of work to compute. There are all sorts of confounding factors: during World War Two, for the US Army, infantry made up about 20% of the personnel (half were in logistics, various other combat arms like artillery, tankers, engineers etc. made up the balance) but did the vast majority of the dying: something like 80% of US Army deaths came from that 20% of the force. So is the combatant count just infantry (and the small number of other combat arms who were forward of the gun line)? Similarly, about half the total US deaths during WW2 came during the Northwest Europe campaign (D-Day to V-E Day, France-Low Countries-Germany). The other half of the deaths came from the entire Battle of the Atlantic, the Bomber Offensive, Mediterranean and Pacific combined. So those 11 months were much deadlier than the rest.

This is the advantage of the straightforward monthly average, it can be computed in five minutes from Wikipedia. Trying to get more detail quickly becomes a whole bunch of tricky choices that reasonable people can disagree on, but which leave you with wildly different numbers.

> First, since you mentioned "Americans and the rest of the world"

Given that we’re discussing American test pilots/fighter pilots, this makes sense.