To understand why electrons are attracted to the proton, you just need to look at the charges of those quarks.
In elementary units an up quark has a charge of +2/3, a down quark a charge of -1/3. 2/3+2/3-1/3 = 1. So a proton has a net charge of +1. Meanwhile an electron has an electric change of -1. Opposite charges attract and so the electron and proton are attracted to one another.
As for the proton and the neutron, they are attracted by the residual strong nuclear force. This is a force between any particle made up of quarks, regardless of electric charge as it is a separate force entirely from electromagnetism.
Neutrons are *electromagnetically* neutral. But there are other forces out there besides the electromagnetic force. For neutrons and protons, there is the strong nuclear force, which is much greater than that of the electromagnetic force, but only operates on much smaller distances.
Both neutrons and protons are made up of quarks, as you note. The up quark has a positive 2/3rds charge and the down quark has a negative 1/3rd charge. This means the proton has an net positive charge of 1 (2/3 + 2/3 – 1/3 = 1) and the neutron has no net charge (2/3 – 1/3 – 1/3).
Each electron has a net negative charge of 1, and is electromagnetically attracted to the positive charge of the proton.
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