In Black Swan the movie, does Nina kill Beth at the hospital?

When Nina visits Beth in the hospital, and Beth is sitting in her
wheelchair and she starts stabbing her face with the nail file, is it
really Nina doing that?

Also, when Nina is in her dressing room during the opening show, and
she stabs Lily with the glass, what's the metaphor here? Like...why is
she supposedly killing Lily? And how does she just imagine all of that
happening when all she really did was stab herself? Like how can a
person just imagine all of that?