The DA40 is not "complex" as per the FAA definition even though it has CSP, so to be complex or to get the complex endorsement you need to have all three.
Regarding the High performance endorsement, yes it is indeed OVER 200HP "on any one engine during any phase of flight". This means that a 200HP Seneca II is indeed high performance despite only being rated to 200 HP at sea level...because the Turbocharged engines actually develop 215 HP at altitude apparently.