This is a several part answer.
1. A vector file
The correct term is "vector file" or "vector format", not vector scale. It is one that can be edited and scaled. Internally is made of formulas and data.
One example is a circle. You can define the circle position, radius, fill color, and edge color. To scale it you simply change the radius information.
Some examples of programs that do this are graphs from a worksheet, shapes made in presentation software like PowerPoint, or more complex illustrations made in (sorry if I am redundant) vector Illustration software like Illustrator, Corel Draw, Affinity Design, or Inkscape.
The logo of this website is a vector. https://cdn.sstatic.net/Sites/graphicdesign/Img/logo.svg?v=c784e64edfd8
2. What is not a vector file
If you take a photo with your cellphone of the same circle you can not edit it anymore. You do not have a circle, but a bunch of pixels arranged in the shape of a circle. You can zoom in but it will make the image blurrier.
My avatar is raster: https://i.sstatic.net/B1JLd.png?s=256
3. What they need
A good quality image that will look good when printed, and some room to adjust it to the project.
4. What you need to do
Define if you have your source files, instead of giving them, for example, a screen capture.
What does this mean if I have only images?
But the truth is that you need to hire a designer, to see if they can export the files to the proper size or re-make them in the proper quality or format.
5. They have no idea
For me, it is really funny the word salad of the requirements. I am not referring to your post (Of course is great that you want to clarify your doubts). I am referring to what they assume they want.
You can continue to read, but I do not want to confuse you more.
Let us see the word salad
Also, do these guidelines imply ... 7791 pixels by 4724 pixels?
If you have pixels, then it is not a vector. This is an alternative size.
Width = 8.5 inches OR Width = 7791px (In-between) Height = 11 inches OR Height = 4724px (In-between) Pixels/Centimeter = 300 (DPI) (minimum)
The math is really simple.
If you have a letter size page at 300px in every inch you have
8.5 x 300= 2,550px
11 x 300 = 3,300px
Pixels/Centimeter = 300 (DPI)
- DPI is dots per Inch, not pixels per centimeter.
- The correct unit is PPI, Pixels per inch. And the common number is 300 PPI.
- If you make the conversion to PPcm is 300/2.54 is 118 pixels per centímeter, but NOBODY in the planet uses pixels per centímeter. And I live in a non-anglo-unit country.
Halftone image type ... with color mode being RGB or Grayscale.
A facepalm. This is getting worse. Nobody sends a Halftone image. What you use is a "normal" photo or image. They are usually RGB. The photos from your cellphone, a screen capture, a file downloaded form the web. A grayscale image is a simple conversion to grayscale.
A halftone is made on a VERY specialized process that can ONLY be defined by an expert on the output, normally a part of the print process.
A halftone is NOT RGB or grayscale, is a 1 bit image.
The resolution of a halftone is not 300PPI, is normally a multiple of that. 600 or 1200PPI.
It can be also be used as an effect for stylistic purposes. Only in that case can be RGB or whatever.
The following file formats can be
accepted (our preference in order of appearance): PDF, PPT, Word, Excel, PNG, CDR, IA, EPS, TIFF, JPG
Yup, you do not have a salad... you have a smoothie. They mixed all together in a blender.
PPT, Word, Excel. They want the source files to extract the elements they need.
CDR: Corel Draw, AI (Not IA): Adobe Illustrator. These are specialized drawing software.
PDF, EPS: These are delivery formats. You make something in some other program, Word, Corel, or Illustrator, and Export it to PDF to deliver a fixed file that can be viewed in a lot of platforms. EPS is just an old format not really used anymore. Just use PDF.
PNG, TIF, JPG: are raster formats made of pixels, not vectors.
Corel Draw, Illustrator, Power Point, and even Word an Excel can have also raster images inside. You can copy and paste your photo inside any of them.
The point of a "vector format" is that the image is generated inside them, not imported.
If you have a blurry JPG photo of a shape, copy-pasting inside Word will accomplish the "accepted format" but the shape will still be unusable.