Firstly, as someone who is almost 30 as well and who got rejected at all the places I applied to last year, I can tell you that it is possible to apply again after getting all rejections. You need to have good support - as the application process takes a toll not only on us, but on our families as well. You also need to have recommenders that believe in you and will be willing to support you again.
Secondly, calm down. You sound like you put together a really good application and I think you should have a decent chance, even at schools that take only 10% of applicants. You have publications - the majority of applicants don't have that, so that alone will make you stand apart from most applicants. And if your publications are good, you probably would stand an excellent chance at getting an admission at most places.
That said, it is possible for even an exceptional applicant not to be admitted. There are a host of reasons that could cause this such as, your interests might not fit well with the department's, the POI you would work with might not have funds for a new student or the school might think you're such a good applicant that you wouldn't go there so they don't even bother with an admit. If this does happen, and it's still early in the application process, you could strengthen your application and reapply to a broader range of schools to give yourself more chances. Some schools have Spring/Winter admission, so if you did have to re-apply, the extra wait might not be long.
So my advice to you would be,
i) don't worry about that now - it seems you have a strong application and it's still early in the season - unless your schools have all finished making decisions?
ii) if you don't get admitted, don't take it personally since many strong applicants don't get admitted on their first try. You can reapply and use the extra time to strengthen your application and increase your odds of getting admitted.
Best of luck!