While economics is an important field, at the undergraduate level, very little depending on what you are wanting to do with the knowledge. For example, if you wanted to understand the economics of hedge fund contracts, that would be under microeconomics and financial economics. If you wanted to understand top-down portfolio management then you would study general macroeconomics and financial economics. You would be better off reading in finance than economics.
Economics is the study of how people make choices given limited resources. Finance is the study of how to get the right amount of money to the right place at the right time and to account for risks to those strategies. Both are important, but finance would likely matter more unless your concern is policy related or behavioral.
1) To some extent, all of them, but primarily financial and monetary economics. Financial economics is the study of the deferring of consumption from today into the future. Monetary economics is the study of how fixed contracts (such as money) impact the real economy and so includes financial intermediation.
2) I would start with Bolstad's Introduction to Bayesian Statistics and Dennis Lindley's book "Making Decisions," and a follow up on Bayesian Econometrics. Lindley's textbook is what I call a 13th-grade book. It isn't college, it isn't high school, but it gives you a feel for the thinking. You will need calculus through multivariate integration to get through Bolstad's book. You should also separately read any introductory statistics text and a standard econometrics text. I am recommending the Bayesian first because it will make a lot more sense as it is likely how you think about the world now and it is more useful in the hedge fund world. Frequentist statistics are somewhat backward to how people view the world. These would be your preparatory courses.
After that, I would either pick up a game theory textbook for non-mathematicians or have you pick up any introduction to set theory textbook plus a rigorous game theory book for economists. If you get the basics of sets and orderings, then game theory is mostly just a set of fixed point theorems. I would then have you read Parmigiani's textbook on Decision Theory.
Once you have done that, it depends upon what you are wanting to do with the knowledge. For example, you could look at "Financial Economics," by Jurgen Eichenberger. Again, it all depends on what you want to complete by doing this. Hedge funds and the like are rarely taught at the undergraduate level unless they are taught as special topics to any meaningful depth. In the giant scope of all human behavior, they are actually a very small subset. Actually, in terms of behavior, they probably fall into the preposterously small subset. It is such a small group of people, although they may be important, that the economics of stamp collecting may represent a larger group of people. Undergraduate education is broad and general because nobody knows ahead of time which elements will be important.
Hedge funds, unless you are interested in regulatory aspects which would also involve the economics of legal systems, are a very narrow topic. If you are looking for a job, you are better off getting a graduate degree. But I will warn you, in the related field of venture capital, they asked someone what the job was like. Their response was "it was like coming in every morning and climbing a mountain made of broken glass on your hands and knees." That will be true in hedge funds as well, maybe even more so.
To get a better answer, you need to think through what your real underlying question is. If it is to learn the economics enough to get a job, then make sure you have one semester of computer programming and differential equations. You should also get two semesters of introductory accounting textbooks. If you are just curious about a policy topic, such as the impact of hedge funds on national systems of production, then that is a very different set of books.