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.
1) No, reflection, emission and absorption are all distinct processes. Reflection happens when an incident wave hits an interface (like a typical air-glass interface). Due to this discontinuity in the propagating medium part of the wave is transmitted and part is reflected. So no incident wave implies no reflected wave.
2) The color of an object depends on all frequencies it doesn't absorb and how sensitive your eyes are to those frequencies. Everyday objects don't aborb a whole range of frequencies, so their color is the combination of all non-absorbed frequencies.
3) No, the emission spectrum is solely dictated by the eletronic states of the atom and their interactions with the rest of the material. The problem of using reflected light to charecterize the spectrum of an atom is that any other losses (like scattering) in the medium will also take energy from the wave. So, your reflected wave will come with information about the whole medium and not of just a single atom.
Best Answer
There is some confusion of terms in the question.
A photon is an elementary particle in the standard model of particle physics, see table. Its mass is equal to zero, it is a point particle, and its energy is equal to $h*ν$, where $h$ is planck's constant, $ν$ is the frequency for the classical electromagnetic wave, light, that emerges from a large number of such photons. As far as the photon is concerned the term "frequency" has no meaning other to identify its energy.
the electron is also a point particle in the same table with a fixed invariant mass of 0.51099895 MeV, which is invariant. In no way a free electron can absorb a photon, a photon can scatter off an electron, its energy becoming less. Absorption of photons can only happen in scatters of photons with bound electrons in energy levels, in atoms, molecules and lattices . It is the whole atom that absorbs the photon, the electron changing energy levels due to the absorption. The energy levels have a width, and that is reflected in the ability of atoms to absorb photons with a $Δ(E)$ in energy, which width is directly related to the frequency of the light of multitudes of photons.
The colors of the spectrum are not one to one with the colors our eyes have defined. The spectrum from a crystal have specific frequencies that we have named with the color we see, and there, there is a one to one correspondence, frequency to color. Note there is no "white" in the spectrum:
But our eyes can see the same named colors with a combination of light frequencies, called color perception:
The color perceived at point T , comes from a combination of frequencies, and many different pairs give the same perceived color. White in this plot is around the achromatic point. Please read the link for details.
In summary, white is not a color in the visible light spectrum, many frequencies could make up the perception of white color, which means that photons of a large variation in energies make up the white color.
The figure shows how the frequencies combine to give the perception of white. One needs many photons for our eyes to be able to perceive them, but even a few hundreds can give a signal to the brain, this link might interest you.
A single photon cannot give the perception of white.
Hope this helps.
Edit: Since comments might disappear if there are too many, I copy here a significant comment by @PhysicsTeacher: