Does a RAW file in Photoshop contains all the data only while in Camera RAW or at all times in Photoshop?

Typically, RAW files are not changed during image processing. If you operate in Photoshop and save in Photoshop's native format (.psd, I believe), all the information from the RAW will be retained, as will any layers, etc. applied to the image. You could easily change/undo anything you did. If you save as a 16-bit TIFF you'll have utilized all the RAW information as well as the effects of the layers, but going back is difficult/impossible. If you save as an 8-bit JPG, you will lose data that cannot be recovered (That sounds bad, but that's the point of JPG, to make files smaller).

Alternatively, RawTherapee won't affect the RAW file either, but will save any edits simply as plain text rather than creating a new file format for edited pictures.

First, let's remind ourselves of what a raw file is. It is a set of single luminance values for each pixel on the sensor. As such there is no color information to a raw file. Color is derived by comparing adjoining pixels that are filtered for one of three colors with a Bayer mask. But just like putting a red filter in front of the lens when shooting black and white film didn't result in a monochromatic red photo, the Bayer mask in front of monochromatic pixels doesn't create color either. What it does is change the tonal value (how bright or how dark the luminance value of a particular color is recorded) of various colors by differing amounts. When the tonal values (gray intensities) of adjoining pixels filtered for the three different colors used in the Bayer mask are compared then colors may be interpolated from that information. This is the process we refer to as demosaicing. How much bias is given to red, green, and blue in the demosaicing process is what sets white/color balance. The gamma correction and any additional shaping of the light response curves is what sets brightness and contrast.

The image you see on your computer screen when you are editing a raw file is not the raw data. It is a preview image generated by the raw editing application you are using by applying your current settings to the raw data that results in the image you view on the LCD. When you move the sliders or change the numerical values for various settings the raw data is not changed. What is changed is the way your editing application interprets and displays a portion of the information from that data.

In most editing environments the image on your screen is an 8-bit image very similar to a jpeg image, but the demosaiced data used to create that image may have higher bit rates. When working with multiple images of the same scene exposed at different levels to create an "HDR" image we often use applications that create a 32-bit floating point file. But the application reduces this 32-bit file to 8-bits when we see it on our screen. TIFF files often use 16-bits per color, but those 16-bits are not the same type of information as the 12 or 14-bit monochromatic luminance value recorded for each pixel well on a sensor contained in a raw file. The 16-bits in the TIFF file have already been demosaiced/converted to an RGB raster image format.

Apart from Adobe Camera Raw (or an application such as Lightroom that internally uses ACR to demosaic raw files and display them on your screen), the tools in Photoshop and other integrated Adobe products only work on the data after it has been converted to a color raster image. If you want to make changes to the way the raw data is interpreted as it is demosaiced into a color raster image you must do it before the raw data has been converted to a raster format such as jpeg or tiff. Just as with Lightroom, from within Photoshop you do that by accessing the raw data using ACR to redo the demosaicing of the raw data to create a different raster image to which other adjustments and layers are then applied.