It's ok as long as the types don't leak into the public API when the code is distributed as a library. But yeah, it looks like a leftover bad habit from pre-C99 times (I suspect the author is on Windows where MSVC was very late to the C99 party), and Microsoft also recommened for a while to build C code via the C++ compiler, which is where the "cast result of malloc" habit might come from.

To make them easier to type and more aesthetically pleasing

Typedefing uint32t to u32 etc is extremely common

They wanted shorter aliases for them to make their code clearer, I suppose.