Neither the photon nor the electron are classical particles and there is no Newtonian picture of the process. Instead you have to imagine relativistic fields that describe the probabilities to detect photons and electrons in different spacetime points. Before the absorption there is a non-zero probability to detect the photon and the probabilities of the electron field are roughly those predicted by the Schroedinger equation for the low energy state of the atom. After the transition the probability to detect the photon is mostly gone and the electron distribution is now in a higher state.
One has to be very careful even with this picture, since one can't do continuous measurements on this system without disturbing it. What these distributions really mean is that we prepare one photon, then perform one measurement on either the photon or the electron. We repeat this experiment many times and then we plot the probability distribution as a function of time. This would have to be a multidimensional plot because of the ways the parts of the quantum system interact. Unfortunately people are not very good at recognizing the finer details of such multi-dimensional phenomena. Whenever we talk about these probability distributions and we show images in books, the problem has already been greatly simplified for our own convenience. From the perspective of human perception it is probably next to impossible to visualize the entire process without some simplification or loss of information.
Another way to get atoms to emit light is to shine white light on an atom and the electrons would absorb the photon if the energy of that photon was equal to the energy difference between the energy levels. And the electron would jump to the next energy level and be absorbed. All other wavelengths do not have sufficient energy to allow an electron to jump to the next engery level so they will pass though the atom unchanged.
What is unclear to me is what you mean by being absorbed. As I say below, an electron cannot be absorbed, which is what I think you are implying above, but a photon, as the force carrier between electrons, can be absorbed and emitted.
I think there are duplicates for the other related questions in your post, so I will stick to the last two in this answer.
Why is it that the electron loses energy when it jumps to the next energy level
Let's take the common usage of the word jump as upwards. So in this above case, the electron gains energy. It loses energy when it falls back down to a lower level.
I have to admit that I don't like using words like jump and fall, because they are based on the Bohr model of the atom, which is not correct in almost every aspect.
So let me give you two pictures, one of the old model, which your question is based on, and one of the more modern picture.
The Bohr model (of 100 years ago)
The Orbital Distribution Density model
The electron will tend to lose energy if it can, by emitting a photon of the correct wavelength, that enables it to transition to a lower energy level, but if that lower level is already occupied to the maximum amount, then the electron is forced to stay at a higher level.
The difference between the pictures is the the Bohr model assumes a particle structure, whereas we now think in terms of the probability of finding an electron in a certain region, so we cannot be as definite as in the earlier model. Also, when the transition from one level to another occurs, it is not a smooth transfer like a car changing lanes, it is for a time a more chaotic operation, with the electron (or rather its' likelyhood of being found) bouncing around the place until it settles into a lower orbit.
In the first example the electrons moving with current gives energy to the electron in the atom. So the electron in the atom absorbs the moving electron? If so how is this possible because they are both negative?
There is no question of an electron absorbing another electron. Instead, by means of photon emission, momentum can be transferred between electrons, bearing in mind the conservation laws regarding energy and momentum.
An example of this is a Feynman Diagram:
Where the wavy line represents energy and momentum being transferred by means of a photon.
Best Answer
You are asking about electron de-exitation, and there are basically two main types of processes involved, in any case, the electron/atom system moves to a lower energy level if there is such a lower energy level available:
In this case the excited atom/electron system transitions to a lower energy level, while emitting a photon. This form of emission is mainly a QM phenomenon, and you are asking why it happens. In this case, the answer is quantum mechanics itself, a trigger for the process can only be understood with the explanations in QED and vacuum fluctuations.
https://en.wikipedia.org/wiki/Spontaneous_emission
In this case, an incoming photon of a specific frequency can interact with the electron/atom system, and cause it to transfer to a lower energy level.
https://en.wikipedia.org/wiki/Stimulated_emission
It is very important to understand that I mentioned everywhere a photon emission but there are mainly two types of such processes, radiative and non-radiative transitions. In the case of the latter no photon is emitted.
Just a note, there are other forms of transitions, like fine and hyperfine transitions too.