(I am the Graduate Coordinator for the mathematics department at the University of Georgia, which is consistently ranked around the 50th best mathematics department in the US. I also received my PhD from Harvard, which is consistently ranked in the top three.)
Zeroth of all, if you think that University of Chicago is a "second tier program," then I think your tiers are too small to be meaningful. I am very familiar with both Chicago and MIT and think these departments are comparable in quality according to a broad range of metrics.
Also will age a disadvantage (I'm 28)?
Absolutely not. Age discrimination is illegal and also not truly not done in American graduate programs. Moreover I am not even sure that you have to disclose your age, but as someone who has been most directly involved in graduate admissions in my department for the last two years, I can assure you that the admissions faculty almost never notice the age, let alone take it into account.
Edit: My GPA on the US scale is around 3.6 plus/minus 0.1.
That is indeed not a great GPA relative to your competition. The median GPA for applicants to UGA is, I believe, slightly higher than this, and I shudder to think where UGA would rate on your "narrow tier" system: eighth tier, maybe? The very top graduate programs have their pick of the litter: they could, if they wanted, enroll a class full of candidates with essentially maximal GPAs, GRE scores and recommendation letters. And this is what they largely do, while also looking for candidates who are exceptional in their research achievements and promise. So, for instance, a place like Harvard would take a candidate with a 3.6 GPA if they had written a truly significant research paper.
Third: the GPA is just one number, and as a number, 3.6 is not so bad. With that GPA, a more important question is: in which courses did you do well, and in which did you do less well? If the less good grades are confined to the early years of the program and your transcript shows a clear upward trajectory that is supported by the recommendation letters, then many programs will not view a 3.6 GPA as a negative.
Fourth: we all want to go to the best programs we can (as we should!), but when it comes to your admissions strategy, you should take a more conservative approach of applying to schools in multiple tiers. As a quantitatively minded person, I recommend that you tackle the "Fermi problem" yourself: how many students in the world do you think are interested in doing a math PhD at Harvard / Princeton / MIT / Stanford / Chicago / Berkeley / Oxbridge and have strong but not perfect backgrounds from internationally renowned institutions? How many spots do each of these schools have per year? I think you will find that the competition is fierce. You might get in -- and I heartily agree that you certainly won't if you don't apply, so I think you should apply -- but there are going to be a lot of other, similarly (well!) qualified candidates.
By the way, schools "as far down" as UGA still have very strong programs in certain areas, and a strong student can do very well at these places. At UGA some of our PhDs have gotten NSF postdocs, one of them is now a tenured faculty member at one of the elite schools you mentioned, and so forth. UGA is internationally renowned in algebra, geometry, number theory and topology. I could say similarly strong things about most other institutions at the same level on the rankings --e.g. Boston University, University of Virginia, Dartmouth, Emory, University of Massachusetts -- they have some tremendous strengths. In summary, the number of really strong graduate programs in the US is larger than you might think, especially as an international student. Please keep that in mind.