The Rutherford model of the atom didn't respect any quantization: it was a classical planetary model. The Bohr-Sommerfeld model had the quantization of the allowed orbit from your first picture; however, you conflated these two models and spoke about "Rutherford-Bohr" model which has never existed.
The third thing that you conflated is the actual quantum mechanical equation that describes the atom correctly - in the non-relativistic limit - while neither the Rutherford model nor the Bohr model are correct in details.
The states $1s,2s,2p,3s,3p,3d,\dots$ that you refer to on your second and third picture only exist in the correct quantum mechanical model that predicts three quantum numbers for the electron, $n,l,m$ (if we ignore the spin). The Bohr model only predicts (incorrectly) one quantum number $n$, so it would only have states $n=1,2,3,4$ and no extra $s,p,d$ labels that distinguish different values of $l$. In some sense, the Bohr model has angular momentum $l=n$ and it doesn't allow any values $l<n$ while the correct quantum mechanical models only allows $l<n$ but all of them - it predicts $l=0,1,2,\dots n-1$.
So you should recognize the different models. The Rutherford model is classical and hopeless - and only included the insight that the nuclei are smaller than the atoms. It didn't know anything correct about the motion of the electron.
The Bohr-Sommerfeld model knew something "qualitative" about the motion of the electron, namely that there was something quantized about it, but it was still too classical and it was the wrong model that only happened to "predict" the right energies after some adjustments but this agreement for the Hydrogen atom was completely coincidental and related to the fact that the Hydrogen atom may be solved exactly (and the answer for the allowed energies is very simple).
So the answer how you can see $1s,2s,2p,\dots$ states in the Bohr (or even Rutherford) model is obviously that you can't see them because the Bohr and Rutherford models are invalid models of these detailed features of the atom.
If you decided to learn quantum mechanics and abandoned the naive ideas such as the Rutherford and Bohr-Sommerfeld models, you could also discuss other properties of the electron states in the Hydrogen atom. For example, the states $2px, 2py, 2pz$ from your first picture are particular complex linear combinations of the usual basis of states $2p_{m=-1},2p_{m=+1},2p_{m=0}$. In fact, $2pz=2p_{m=0}$ while $2px\pm i\cdot 2py = 2p_{m=\pm 1}$, up to normalization factors.
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A charge radiates every time is accelerated. The power radiated is given by the Larmor formula. Putting this into the introductions to the motion of a charge in electromagnetic fields would be a meaningless complication, as much as considering air friction. But yes, a charge in a magnetic field would not spin indefinitely, even in vacuum.