PG,
rumpfy provided a nice summary of some important and relevant facts about fiber optic communications. Overall, your questions are probably answered here, but I can take a run through the questions to give just another viewpoint, in case this helps you. I am likely repeating some of the information given above.
Q1: Suppose two laser beams being used for the purpose of communication cross each other vertically. Would there be any interference? Would the information contained in those laser beam be affected?
Generally, in linear media, you do not expect laser beams to interfere (EDIT: on rereading my response I'm realizing we are both using the word "interfere" to mean cross coupling with each other. However, a typical use of the word "interference" in laser terminology is related to "interference patterns" which are the addition of fields which creates constructive and destructive interference. Obviously, laser beams can interfere in this way in linear media, but I assume this is not what you are asking.). Separate signals will be independent based on direction, polarization, spacial mode pattern and frequency, and will not interfere, in principle. However, the real world does not perfectly obey our idealization, and there can be cross coupling of signals. Separation by polarization and spacial modes is tricky and there is often cross coupling due to fiber imperfections. However, frequency and direction tend to be very good ways to separate different signals. The only way for these separate signals to interact is through one of the many types of non-linear processes that are well known. To keep these effects insignificant one just needs to make sure that the signal power is low enough to not induce significant nonlinearity. However, nonlinearity can happen at relativly low power because the fiber confines the light to a very narrow cross sectional area, which makes the light intensity very very high, relative to the actual power level.
EDIT: I just realized that I should have mentioned that Rayleigh backscattering can cause a signal going in one direction to be reflected into the backward direction. This is a distributed reflection, but it can cause interference. Since Rayleigh backscattering is so prevalent in fibers, liquids and gases, it is worth mentioning separately.
Q2: We know that radio communication is affected by electromagnetic interference. I think this interference comes into play at the receiving end such as antenna where both information radio signal and interference radio signal is picked up by an antenna and this combined reception of both signals produces a new noisy signal at the receiving circuit. Do I have it right?
That is certainly one way, and probably the most significant way in practice.
As far as "pulsed" versus "not-pulsed", laser diodes are usually run in continuous mode, but they can be pulsed in principle for different applications. The continuous laser is then modulated. You could say that the modulation is a form of pulsing too, but this is just a terminology issue. The idea of "pulsing" a laser is usually meant to describe the trick to get lasing in a material that does not allow continuous lasing very easily (such as a 3-level system)
Q3: What kind of laser is mostly used for optic fiber communication? I believe it's a laser diode which provides continuous laser beam and not a pulsed one, right?
Yes, laser diodes are the most practical lasers used in communications. They are specially designed for this use, and come in varying degrees of sophistication in design, depending on the application.
Q4: Which laser is most popular for optic fiber communication in terms of wavelength? Is it red one? Can they also use infrared laser in optic fiber communication? Ultraviolet lasers also exist so why not use them because they can provide higher data rate than visible light lasers?
It all depends on the fiber type. There are plastic fibers designed to be used with red light (or visible light). However, most glass based fibers (silica based being the most practical and common) work best in the infrared. The first fiber optic systems used 800-900 nm infrared because the sources and detectors were available at that wavelength and were cheap and reliable. Also, due to too much water content in the fiber, longer wavelengths would have had higher loss anyway. But, intrinsically, once water impurities are minimized, the longer wavelengths are better, but eventually molecular absorption (which can't be removed) takes over and the fiber becomes opaque if wavelength is too long.
By the way, ultraviolet light would have too much Rayleigh scattering.
So, the 800-900 nm range is not optimum for silica fiber. Silica has two interesting bands for communications. The lowest loss wavelength is 1550 nm, and the wavelength of zero material dispersion is near 1300 nm. Fiber design can also affect dispersion, so it is possible to design dispersion-shifted fibers that have zero dispersion at 1550 nm and lowest loss at 1550 nm, with 0.2 dB/km loss. But, these are just details. Basically, 1310 nm was the earlier technology that became practical with 0.4 db/km loss and essentially zero dispersion in single-mode fibers. Then, good sources were developed at 1550 nm. At that point, very narrow linewidth lasers were developed to minimize the dispersion problem. So, depending on the application, those are the better wavelengths to use, particularly over long distance. However, 800-900 nm can still be used in cheap multi-mode fiber links over short distance.
In the last couple of decades we've seen the development of erbium doped fiber amplifiers and Raman amplifiers, both which work great at 1550 nm.