Help solve this error (I think?)

[white star]

Professor dropped this and I noticed that C's solving was a bit off but I'm not sure. Thoughts?

[long sluice]

Yea ..

The calculations done for workdone by friction are wrong

Friction is normal times coefficient

Normal in this case will be

Force if gravity (he has taken into account) and also the external vertical force being applied ( he missed it)