Of course? You simply undefine NDEBUG in your library
Its trivially easy to guarantee that an assert always runs, and its well defined behaviour according to the spec. There's no reason not to if you want to use asserts in a way that guarantees that they always fire, which is a supported use case. Its common practice
There's no equivalent for contracts
No, it's not. Don't do that. Someone (like me) will replace assert.h wholesale and it will not behave the way you expected. Always define your own internal macro and always provide facilities for the user to override it.