Who generally connects the animations into the player? A programmer or an animation(UE4)?

The tools allow for either to do it, or even for others like a designer to do it.

In most projects we have followed a pattern where the programmer put together the basic elements and flow using placeholders, then the animators replaced the placeholders and added some animation details if needed. Animators and programmers should generally be working together on bringing objects to life.

However, that isn't universal. Sometimes designers do that work, sometimes the animators do the work. But I've found that since it is the programmer that must manipulate the data, having the programmers get the framework in early tends to have the least problems. Other disciplines do their best, but it often doesn't match the programmer's logic.