I'm TommyGun's author, my name is Tony.
Welcome here!
I was wondering if you could provide me with the following screen mode information.
Very hard answering to your questions, because the Nick chip (graphical chip of the Enterprise) are very flexible.
Nick documentations.For example you can programming the Nick for displaying any CPC 464 modes, or attribute graphics of the ZX Spectrum and many more!
1. The number of screen modes - ie. Low Res, Hi Res etc
-Pixel graphics mode.
-Low Res pixel graphics mode
-Attribute graphics mode (similiar to the ZX Spectrum graphics)
-Character 64 mode
-Character 128 mode (most commonly used character mode)
-Character 256 mode
3. Number of colours per mode
You can select 2,4,16,256 color modes for pixel graphics modes
At the 256 colors mode, you use directly the 256 colors.
At the 2,4,16 colors you need to use palette colors.
The palette define 8 colors. All palette color can be any of the 256 colors.
In a 2 colors mode you use the first 2 color from the palette, in a 4 colors mode you use the first 4 colors.
In a 16 colors mode use all of 8 colors of the palette, and the second 8 colors defined by the FIXBIAS register.
The FIXBIAS select one 8 colors block from the 256 colors, this means, the col7-col15 in the 16 colors mode can be a 0-7 or 8-15 or 16-23,etc
The attribute graphics mode use 16 colors.
The character modes are more complicated, now I only write the most popular, definied by the operating system. This is a Character 128 mode, can display 4 colors: character code 0-127 displayed with the first two colors of the palette, character codes 128-255 displayed with the second two.
The border can be display any of the 256 colors.
2. Dimensions of each mode
This is the hardest question!

At the default character mode you can write 40 characters to each line.
Horizontaly one character lenght is the minimal display size.
At Hi-Res graphics, 2 colors mode: one character size means 16 pixels horizontaly.
You can define about 1-44 character wide screen, more than 42 then: no border visible
For example: emulate CPC video modes, then need to use 40 characters wide screen, emulating ZX Spectrum Screen: 32 characters wide.
The resolutions:
If you use the standard 40 characters wide screen at the hi-res 2 colors graphics, then you got 640 pixels horizontaly.
The Lo-res is a half of the Hi-res: 40 characters wide lo-res 2 colors: 320 pixels horizontaly.
If you double the numbers of the colors, the the resolution go down to half.
Summary horizontal resolutions (using 40 characters wide screen):
HIRES 2: 640
LORES 2: 320
HIRES 4: 320
LORES 4: 160
HIRES 16: 160
LORES 16: 80
HIRES 256: 80
LORES 256: 40
Attribute graphics: 320
The vertical resolution, not affected by the video modes or colors.
You can define the vertical size from 1 line to about 260-270 lines. The empty are is filled with the border color. If you define about the maximum size screen, you can totaly hide the border. (The operating system define 252 lines.)
Some examples for summary: 640x200 2 colors, 640x240 2 colors, 320x200 4 colors, 320x240 4 colors, etc can be used on the Enterprise.
4. The default palette for each mode - ie. the RGB for each colour in the palette and what ones the modes default
No default palette. When you generate the Line Parameter Table, then you define them. But if you want, I can write what is default definied colors by the OS.
In the Nick documentations, you can see
generated the colors, if you want I will calculate the 24 bit RGB code of each Enterprise color.
5. And the display mode names (ie. what you want to see in the display list combo box)
The commonly used names comes from the IS-BASIC:
GRAPHICS HIRES 2
GRAPHICS LORES 2
GRAPHICS HIRES 4
GRAPHICS LORES 4
GRAPHICS HIRES 16
GRAPHICS LORES 16
GRAPHICS HIRES 256
GRAPHICS LORES 256
GRAPHICS ATTRIBUTE
TEXT 40 (this is the character mode, using character 128 mode of the NICK chip)
(TEXT 80 is exist in the BASIC/OS but it is not a HW character mode, use Graphics Hires 2 mode, and the OS copy the pixel datas from the character map to the graphics memory)