You're asking about two distinct phenomena. The difference between them is subtle, and I think there is some context missing from the second question that you quote, which makes things more confusing than they need to be.
When the neutron star forms, most of the protons and electrons combine together to form neutrons
This is mostly correct. The process is known as "electron capture," and the full reaction is
$$\rm p + e^- \to n + \nu_e$$
The other particle in the final state (represented by a nu) is a neutrino. The neutrino is an uncharged, very low-mass electron-like particle, in the same way that neutrons and protons are different charge states of the same sort of particle. So far as we know, in physics, the number of electron-like "leptons" and the number of proton-like "baryons" isn't changed in any physical process. The neutrinos play an important role in the dynamics of the stellar collapses where neutron stars are formed, but in some authors who write very elementary explanations of neutron stars will leave the neutrinos out of their descriptions. There are advantages and disadvantages to this approach; your confusion here is one of the disadvantages.
A neutron is formed by an electron and a proton combining together, therefore it is neutral: true or false? Answer: false
This is a fundamentally flawed true-false question, because it makes several statements at the same time, some of which are correct. The question I was expecting to find here, based on the title of your question, was more like
The neutron is an electron and a proton that are "stuck together" somehow. (Answer: false)
We have another name for an electron and a proton that are semi-permanently "stuck together," and the dynamics of that system are very different from the dynamics of the neutron.
When you "combine together" macroscopic objects in ordinary life, the things that you combined are still somehow present in the combination. But in particle physics, the situation is different. The electron-capture process that we're talking about here fundamentally changes both the baryon and the lepton parts of the system. To the extent that a neutron behaves like a composite particle, it behaves as if it is made out of quarks.