Do electrons surround the nucleus

Answer 1

In simple models, yes. They do.

In a more correct and more complex model, it is not possible to determine the exact position of an electron at any point, (as they are quantum) but areas of high probability for the electrons to be in exist, they are called orbitals, and yes, they surround the nucleus in a manner of speaking.

In metallic bonding, the electrons de-localise from the orbitals, and they float around the substance. These electrons are not surrounding the nucleus.

Answer 2

Electrons are found outside the nucleus in electron clouds, which are regions where electrons are likely to be found in an atom. However, it is important to note that electrons do not form a fixed path or orbit around the nucleus like planets around the sun in a solar system model.