Do I need a baseline grid for creating a book?

"Okay, thank you! Also, would it be necessary to use the book function for this document?"

While it's not strickly necessary, I find that it makes the job easier. I find that the program runs faster and more smoothly with smaller documents, especially if you are using Index markers. Exporting as a whole book is easily done through the book panel.

"Does a book need to have a specific gutter size as well? Also, what exactly are bleed and slugs?"

Gutter size will depend upon the binding style, and whether or not it will be 3-hole punched. It would be best to ask the company that will do the printing what their minimum values are for margins and gutters.  
Bleeds and Slugs

Bleed: an area outside of the cutting edge of your document -- this is used if you have color or an image that you want to print all the way to the edge of the page. Becasue cutting dies will not hit precicely where planed, it allows an extra margin (around 1/8 inch) so that if the die moves, you will not have a white halo on your finished piece. 

Slug: An area outside the printed piece that is used to convey information to the printer -- colors used, page size, what kind of varnish, ect. (Left image shows bleed, right one shows slug area)

It is a good way to make sure your text align throughout your book.

Here's a video that might help https://www.youtube.com/watch?v=jWH6HDaMkMM

I forgot to address your baseline grid question. What problems is the baseline grid giving you?

If you set all of your paragraph leading as equal to or a multiple of the baseline grid, it should work for you.

Look at the sessions available on Linked-In Learning. If you employer has set you a task as complex as laying out a book in a programs you are not yet familiar with, they should be willing to pay for the training you need to do it well.
Please come back here as you work your way through this project with any specific questions that come up along the way.