I can only speak for myself, and from my perspective on this. A few quick hits;
1) American culture and news dominates our airways. I am subjected to more American content than Australian, and American politics is commonly commented on and discussed on tv, radio and the internet. I'm sometimes surprised by some American's attitudes to this, as it seems like they either don't understand how prevalent this is globally, or just accept that what they consume is of course everywhere without much thought as to why, or the implications. That's by no means all Americans, but it's hard not to wonder how much of the world some folks have seen.
I think there's a bit of give and take when it comes to cultural exchange. At least among nations which are part of the Anglosphere, there's always been a great deal of cultural overlap, as in we tend to watch the same movies, read the same books, listen to the same music, speak the same language (more or less).
I've done some traveling in my time, although perhaps not as much as some people. I visited the Soviet Union during the 1980s, when the Cold War was still going on. They were certainly interested in America, and frankly, a lot of Americans were interested in the Soviet Union (although not necessarily in a positive way).
There are also a lot of Americans who have taken a keen interest in the British royal family, for reasons I've never been able to fathom.
As for America's allies, I think Americans' attitudes tend to be more confused than anything else. Granted, many Americans are just plain ignorant about the outside world, but for those who have a bit of knowledge, they also believe that America's role in the world has been to help defend and liberate our allies. I can understand it if Europeans get irritated by arrogant Americans who say "we saved your butts," but for the most part, a lot of Americans are conditioned to believe that America exists solely to help out and defend other countries in what we call the "free world." So, they honestly can't understand why these same countries can be so critical and judgmental, scrutinizing our every move, and finding fault wherever they can.
So, from Americans' viewpoint, people think "We're just trying to help these countries, yet all they can do is complain." I remember when France and Germany were singled out as troublemakers over their resistance to the war against Iraq, and that's when the whole "Freedom Fries" thing came about.
2) American politics impacts on us very heavily. That is not about caring how America benefits us and our country in the unidirectional way you seem to be suggesting. If the US decides to have a trade war with China, we're impacted. If the US pulls out of the WHO, we're impacted. If the US decides they want to go to war, we're impacted. We don't have the whip hand in the long and generally friendly relationship between our countries. We don't take aid, and we have announced ramp-ups in our military spending that takes it to...surprise, surprise...2% of our GDP. Excuse the overstated analogy, but if you're sitting in the ocean, you take heed of the weather.
I can certainly understand that, and to be sure, the actions of our government also affect us, too. There are a lot of things about our government which truly suck, but a large part of the reason our government sucks is because they're bogged down in trying to manage a global "empire" instead of simply running a country. It greatly saddens me to think of the enormous waste of lives and resources over the Cold War, as well as the various hot wars which it spawned.
3) Some of the issues you face have parallels here, if on a different level. Issues are more global now. I've taken more interest in global politics generally over the last 5 years. The last French election was the first where I spent any time studying candidates in detail, as an example. And if you go to Europe, there is commonly interest and discussion in other countries elections. The American elections might get the most in terms of this, but part of the reason this surprises Americans is because of the limited investment they have (often) in other countries elections and politics.
Ultimately, we non-Americans are interested, and might occasionally offer some good perspectives. If we don't, feel free to disagree or ignore us, but that wouldn't make us any different from some Americans.
You don't need to worry about our voting, but I'd be happy enough to discuss Australian politics with Americans...if I could find a few who spend the amount of time looking at our issues that we spend on American ones.
Well, there are a lot of countries out there, although the internet has made it much easier to get news and information from other countries. I do take an interest in it myself, although I can't necessarily absorb
all the information out there. It's too much to memorize, and on most days, I'm lucky if I can remember where I put my car keys.
On the other hand, sadly, there are a lot of Americans who take almost zero interest in their own politics and elections, much less anything overseas.
And of course, there are plenty of senatorial, gubernatorial, and congressional races taking place, along with local elections all across the country. Most voters might only know about their own ballots in their own district, while they may not know or care what's happening in another part of the country. I mean, I can't say that I'm all that affected by who the mayor is in Peoria, Illinois.