In programming one way at getting better at common problems is solving them in different ways with exercises known as 'kata'. I was wondering, since I'm long out of school, are there available exercises for statistics to increase ones math ability outside of just doing the same problems over and over again out of a textbook?
"Statistics" is a fairly broad field. You could pick up a standard undergraduate probability/statistics textbook, flip to the later chapters, and have a source of new problems for months. (Later chapters on mathematical statistics are often more about proving and less about rote calculations, if you have the right book.) You haven't mentioned much of your background, so this might be appropriate and/or fun.
But since you specifically asked to avoid textbooks, let me offer an alternative suggestion: Lower-level actuarial exams. These exams are mostly about undergraduate probability, and there are a wealth of sample questions available online. Since these exams are taken under time constraints, your "kata" could be finding the fastest way to solve these problems.
I do not think so.
Statistics is a science related to a lot of money. Banks works, governments are functioning, economy flows all because of the 200$ statistics "bricks" sold in universities, that contains thoroughly explained every single aspect that could appear in practice.
If something is not in these brick-books that you can bring to your office as a backup than that is not statistics. You are paid for those exercises done again and again for many generation, not for secret kata's.