Will an absorbed photon always be re-emitted with a different wavelength? And if this is the case, what is the reason that the re-emitted photon (when the electron moves from an orbit to a further orbit) has a different wavelength than its wavelength when it was received?
 A: It is very important to understand that there are mainly two types of interactions between an atom (photons do interact with molecule as a whole too but you are asking about atoms only) and a photon that will cause the photon to lose some energy (there is something called elastic scattering that will cause the photon not to lose energy):

*

*inelastic scattering

In this case, the photon will transfer some energy to the electron/atom system and the photon will change angle. The electron will as you say move to a higher energy level, and the photon in this case does not cease to exist at all. It just transfers part of its energy to the electron, and you are correct, the photon's wavelength changes, increases.


*absorption

In this case, the photon transfers all its energy to the electron/atom system, and the photon ceases to exist. Now there are special cases, where the energy of the photon, now (after absorption) transferred into the energy of the electron/atom system, will not be re-emitted in the form of a new photon, these are called non-radiative transitions.
But you are interested in the case when the energy of the photon is re-emitted and these cases include:

*

*The new photon's energy is the same as the original one's, meaning the electron de-exites to the same energy level (in one step) it originally moved away from.


*The new photon's energy is less then the original one's, and a second (or even more photons) photon is releases with the rest of the energy. This is multiple photon emission. The new photons' energies all together add up to the original one's. The electron returns to the original energy level in cascades. This case can be very interesting, because the cascades can be separated by quite some time in certain cases, causing phenomena like phosphorescence.

Phosphorescence is a type of photoluminescence related to fluorescence. Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. The slower time scales of the re-emission are associated with "forbidden" energy state transitions in quantum mechanics. As these transitions occur very slowly in certain materials, absorbed radiation is re-emitted at a lower intensity for up to several hours after the original excitation.

https://en.wikipedia.org/wiki/Phosphorescence
So the answer to your question is that not all interactions of photons with atoms cause the photon's energy to decrease, but in the case of absorption, the photon itself ceases to exist as a photon and transfers all its energy into the energy of the absorbing electron/atom system. The newly emitted photon (of there is one) will have a wavelength that can be the same or not based on the type of de-exitation.
A: 
Does the absorption of a photon cause a lack of its energy?

If the photon is absorbed, then there isn't a photon anymore. We would instead just have an electron with more energy.

And if this is the case, is this the reason that the photon from the electron when the electron moves from an orbit to a further orbit has a different wavelength than its wavelength when it was received?

This isn't always the case. If an electron absorbs a photon and jumps to a new energy level, if the electron then falls directly back to the energy level it had been at before absorbing the photon, then the emitted photon will have the same energy as the absorbed photon.
However, direct transitions back to the original energy level do not always happen. Depending on the system, sometimes multiple, smaller energy drops occur leading to emission of photons with less energy than the absorbed photons. Additionally there might be other mechanisms by which the electron can first lose energy (such as collisions) so that the emitted photon has less energy than the absorbed photon.
