Universities commonly publish acceptance rates (or you can call and ask their admissions office) as it is a common measuring stick in academics. You might be able to aggregate this information on a ranking website like US News World Report graduate school rankings.
Generally, fields with more funding are going to have more opportunities for funded students, more opportunity for postdocs, and more opportunity for grant funding later in an academic career. Individual fields often have a single publication that tracks relevant statistics about graduate admissions, graduations, attrition, job placement, salary, etc. For example, in computer science we have the Taulbee Survey, which gives all this data.
Graduation rate is studied more comprehensively under the name "attrition rate" or "completion rate". Generally STEM fields have a higher completion rate than humanities and soft sciences. Slide 7 breaks it down by field in the following link: