My understanding is that orbitals are just locations in space where electrons are most likely to be found.
You would have to find someone who knows more about this than I do to get a definitive answer but from a quick bit of research it looks like they are just locations in space where electrons are likely to be found.
I found this on the simple English Wikipedia page:
"Atomic orbitals are the places surrounding the nucleus of an atom where the electrons are most likely to be at any given time. It used to be believed that electrons behaved similarly to the solar system, where the nucleus is like the sun and the electrons orbit like the planets. However, electrons do not go in circles, they move in many different directions. The number of atomic orbitals in an element is defined by the period the element is in. Electrons move between orbitals depending on how fast they are moving and how many other electrons there are."
I would recommend reading the Wikipedia Page on this although is is a bit hard to understand in places.
On your question about infinite sized atoms I guess you could theoretically have atoms with hundreds of electrons and protons but they would be very unstable and you probably wouldn't even be able to practically create them.
The largest atom I have heard of has 118 protons and 118 electrons but that would have only existed for a fraction of a second before it decayed.