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The film on the surface of the beaker forms by condensation from the saturated vapor above the helium bath. This, by itself, has nothing to do with superfluidity. What is speacial about superfluids is that the film, even though it is only a few dozen atomic layers thick, provides a capillary that the superfluid can flow through without resistance.

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The amount of heat added to the system is the integral of the specific heat wrt temperature: $$Q = \int C(T)dT$$ So in the link you give it's just the area under this graph: Although it's true that the specific heat tends to infinity at the lambda point it does so sufficiently suddenly that the area under the graph remains finite. That means the ...

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It means that all atoms are in the ground state, then since potential energy is defined up to a constant you can say ground state has zero energy

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Angular momentum operator in quantum mechanics is defined as: $$\hat{L}=-i\hbar[r\times\nabla]$$ You just need to insert this definition of $\hat{L}$ to $\langle \psi|\hat{L}|\psi\rangle$ (or integral) to calculate. You need to use the integral form for the average of $\hat{L}$ and use numerical methods to evaluate. Also, angular momentum is not of the ...

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