Per the OP's request, I will attempt to explicitly answer his single-sentence questions.
First I need you to define bit rate.
Bit rate is the number of bits per second used to encode a video stream (which itself has an implicit data rate based on the number of pixels (width x height), the pixel depth (dynamic range, color gamut), and frame rate). Here is an example: 1080p24 HD video feeding a 8-bit color (RGB) display theoretically has a data rate of 1920x1080 x 24 bits x 24 frames per second = 149.299200 megabytes per second, or 1.194393600 gigabits per second. Not all HD video is created equal: the full data rate (1.194 Gbps) means every pixel gets every bit fully represented. But it is quite common to encounter 4:2:2 video (which cuts the data rate by a third) and 4:2:0 video (further reducing data rates). You can read about these here: https://en.wikipedia.org/wiki/Chroma_subsampling
And how compressing comes along it?
This sentence is not grammatically meaningful. I'm guessing the question is "how is the compression rate related to the bit rate?" in which case the answer is the compression rate is the ratio of the data rate to the bit rate. If the data rate is 1.2Gbps and the bit rate is 28Mbps, the compression ratio is 43 (rounding up).
What's that 'two frames containing one color, the colors are treated as one color'?
This single sentence contains two completely separate ideas. "Two frames containing one color" likely means that for a region of the image (which may be only a pixel, or which may be a group of pixels), the color of the region is the same from frame to frame. In this case, one need not explicitly encode all of the region for both frames, but one can describe the region for one frame and then reference it in the other frame.
The completely different idea is that multiple colors that we perceive to be very close, either visually or spatially, can be merged into a single color covering a larger region. A blue sky might have millions of very slightly different pixels, but visually they may be represented by perhaps a few dozen different colors of blue. If this is done poorly, we perceive banding of colors, loss of detail, or other artifacts.
Is IT the compressing?
It is one of the means of preparing the image to be more effectively compressed, but not the only one. Said another way...Compressing video by decimating chroma information is one way to reduce video data, but that's often the start, not the end of the compression story. Consumer cameras tend to record video at a rate of about 28 megabits per second. Some, like the GH4, can do up to 200 megabits per second. Those are the bitrates of the compressed video codec.
And, how does increasing resolution while keeping bit rate constant, make the image quality worse?
The bitrate defines how many bits per second you can use to create the illusion of displaying the full data rate of the video format you are trying to represent. The more resolution you have, the more bits you will need to use to represent details that can be discerned in that high-resolution image. The more you try to preserve color fidelity across the whole 24-bit color gamut, the more bits you will need for that, too. It is obviously impossible to perfectly cover every pixel in a 1.2Gbps data stream with a 28Mbps bit rate. In fact, you cannot cover even 3% of it perfectly! But the human eye is easily fooled: if 30 consecutive frames are identical, a clever encoder can spray out a vague outline in the first frame and then successively refine each subsequent frame with more spatial and chroma resolution until, after the 30th frame, what is on the screen is indeed a perfect representation of the unchanging image.
In the real world, video doesn't stay completely still for seconds on end, but neither does it meaningfully change at every pixel location at every frame. (If it did, images would look a lot more like static than anything we could make sense of.) One can measure how much meaningful change exists between frames on average, and how much one can tolerate approximations that allow the same pixel to be treated as the same value between the two frames without destroying the integrity of the perceived image. That can then be calculated as a bit rate.
The bottom line (and answer to the above question) is that increasing resolution while keeping the bit rate constant magnifies compression artifacts without increasing actual image quality. The result is a perceived loss of image quality.
And, what if a video has only 1 Mbps bit rate?
Alternatively, you can define a bit rate, such as 1Mbps, and you can go about trying to encode the change from one image to another by identifying what parts of the image are most important, visually, and then using your bit rate budget to allocate pixel data to those areas first while leaving the rest of the image unchanged. There will come a point when things fall apart: there's just not enough bit rate to faithfully represent or follow the changes of the original data. But obviously if you need to preserve a lot of spatial resolution, you need lots of bits to keep that info correct. If you don't have the bits, you fill in the holes with guesses, and too many wrong guesses makes the resolution suffer.
And how does increasing frame rate while keeping bit rate constant, make image quality worse?
Increasing the frame rate while keeping the bit rate constant means that more individual images must be constructed from a constant amount of information. If you have a 1Mbps bit rate and you try to show 12 frames per second, you have a budget of 83kb to form each frame. If you keep the bit rate constant and increase the frame rate to 120 frames per second, you have a budget of 8kb to form each frame. They human eye can do a certain amount of temporal integration, so there are cases where it is possible to trade off spatial resolution (fewer bits per frame) for temporal resolution (more frames per second), but there are limits. Once the limit is exceeded, perceived image quality suffers.
