Are S orbitals always a cloud around the atomic nucleus and a p
orbitals always nodes?
There are different types of orbitals. They are always mathematical entities, idealised and simplified version of the real physical electrons.
The "simplest" orbitals, and the ones that you usually for Hydrogen or Hydrogen-like atoms, which obey a simple Schrodinger equation whose analytical solutions are labelled by the quantum numbers $n$ and $\ell$. $\ell$ is the angular momentum and so it determines the angular component of the wavefunction. Zero angular momentum, $\ell = 0$, is referred to as the letter $s$, whereas $p$ refers to $\ell = 1$.
So, the answer to your question in yes, for Hydrogen-like atoms (whose solutions are labelled by $\ell$), $s$ orbitals are always a cloud around the nucleus. $p$ orbitals have a node, while $\ell > p$ will have more than 1 node.
Comment on your picture:
Orbitals are just mathematical functions that satisfy a certain equation. So they are smooth, nice looking functions when plotted.
What you have plotted there is a bunch of points that, in the limit of an infinite number, tend to this nice looking smooth function.
Each point corresponds to the same electron whose position is measured multiple times. Each time it is measured, it is found in one of those positions. But there is only one electron. The electron is a wave $\psi$ until you measure it, so it really is this nice smooth function. When you measure it, then it localises (the wavefunction "collapses") to a position. Whose precision and accuracy are limited by the uncertainty principle.
How does an electron jump from one orbit to another?
You need some external interaction that brings enough energy to kick the electron to a higher-energy state, and also brings angular momentum to allow for a $s (\ell=0)$ to $p (\ell = 1)$ change. Usually, it is done with a laser, i.e. you shine photons to atoms, and these induce transitions.
How do the orbits of very large atoms work?
Small atoms, that is with few electrons, are "simple" in that you can ignore the interaction among the different electrons and just work with them independently. I.e., you can think that each electron obeys its own Schrodinger equation, has a nice orbital, and does not care about the other electrons.
But of course they interact repulsively, which changes the shape of the "orbitals" (if one still wants to refer to them as such). There is no analytical solution anymore, but a series of approximations. Hence the different types of orbitals that I linked to before.