Is redshift a reliable means to know how fast an object is moving away or towards an observer? Does wavelength change with distance? How do they know that the change in wavelength can only be caused by the change of speed of the object to the observer?
What if it is an intrinsic property of light to increases its wavelength by the distance? Do we wave any evidence that this is not the case even if we're talking about massive distance like thousands or millions of light years?
Please explain in plain English. I'm not a physics major.
 A: The main thing to note about all of these objections is that virtually everything except for redshift would create a frequency-dependent effect.  This, in turn, would mean that objects would appear on Earth with blurred images or distorted colors.  In the case of an absorbing gas, we would also expect to see absorption lines in the spectrum of any objects observed.  
Instead, what we see is a set of clear, sharp images.  
A: Wavelength doesn't change because of distance. However, because of Hubble's Law (Hubble's relation might be more accurate) the change does have a correlation with distance. It might help you if you knew more about what dark energy and dark matter are: just because scientists don't know what they are doesn't mean they don't understand their effects a little better. Dark energy is actually generally what's causing the Doppler and red shifts of the late. Dark energy is primarily responsible for the expansion of space. However, dark matter primarily interacts through gravity, and thus really only affects light by causing a warping of space time. It's effects can be taken into account if it provides lensing, or redirecting of the light fairly easily. 
If you're asking the question "what about if it traveled through something we don't know about, could it be modified" the answer is always yes, but it's not really a meaningful question. The question can almost always be asked "what if something we can't possibly know about happened," without meaning.
A: For distances out to about the orbit of Neptune, or a little farther, we have alternative means of getting the speed. Parallax and orbit observations and things of this nature. And the red shift and the speed match perfectly. This means for distances of a few cm to distances of several light-hours, all works as would be expected in having light wavelength change according to relativity. Time of flight measurements also work perfectly.
For objects at larger distances we can't do the same kind of measurements. We can't do parallax for other galaxies for example. We have a collection of data that is used to build a pattern. Distances are estimated on the basis of such things as the absolute brightness of certain supernovas. (IIRC it's type Ib, but I didn't check.) And we can do comparisons of what one edge of a galaxy is doing relative to the other, rotating towards us or away. And we can study the light coming from different types of objects to have some confidence that we are getting the picture from a group of objects, like a galaxy, and not some local thing like the front of an explosion. 
So we look at these things and build a picture of how far things are. Then we measure the red shift. And the pattern builds up quite well. Things that are far away have more red shift. Never blue shift.
As Jerry Schirmer mentioned, most of the potential mechanisms for changing the frequency of light other than relative motion will be frequency dependent. For example, we can detect the effect of interstellar and intergalactic gas. This means that when a target produces pulses of light, as for example a pulsar, the pulses tend to show up with the shorter wavelength light first, by a very tiny amount. Astronomers really can be quite subtle. But this effect is far smaller than the cosmological red shift.
And we also see the distance-velocity pattern developing quite smoothly across the entire sky. There are not places where it is far off, neither at different angles nor different distances. So whatever is happening seems to be quite regular and smoothly distributed across the entire visible universe. So it's hard to think how it could be so smooth across such large distances and not be something to do with cosmology.  And we strongly think we understand the large scale structure to be as general relativity says.
