How do I delete a single page in a document without deleting the whole document? Also How can I rearrange pages?

Personally, I would have pointed the OP at the relevant section of the Pages User Guide for Mac, and let them review that information: Intro to word-processing and page layout documents in Pages on Mac - Apple Support

Enable thumbnails and right-click on any thumbnail. If the resulting menu contains four menu items then you have a word processing format document, and you cannot remove individual pages from their sections, nor can you rearrange individual section pages within the same or a different section. Pages page layout documents allow you to remove one or more thumbnails as each of these are discrete pages, and there is no section controlling them. This form of Pages document also permits easy thumbnail dragging for rearrangement. In Page's page layout documents everything must be contained within an object including text in one or more text boxes.

To remove a single page in a Pages word processing document, select View menu > Show Invisibles. Select the specific thumbnail whose page you want to remove, and on its page you select everything (including any page break line indicators and then press backspace to remove. In a perfect world, the page will disappear and you will see the page above or below replace it.

Every so often questions like "why can I not delete a page?" or similar come up here. I think this stems from some misconceptions of what a page or a section really is.

Maybe my explanation will help you and others with similar issues. Might be a bit lengthy and of course you are not required to read it all :-)

Pages (the "program" or "application" or "app", whatever you call it) allows one to create nicely layouted text documents. It has two distinct working modes, text processing and page layout.

Let's first look at Text Processing documents.

In its simplest form one creates a (possibly) very long flow of text, maybe with interspersed images and tables etc. This loooong text flow has nice formatting and is supposed to look good. Now comes your problem: you do not have an equally long sheet of paper. Thus your nice long document needs to be laid out on multiple sheets of paper. You define the size of the physical paper in the page setup dialog.

The sidebar in a pages document window gives you a visual representation of how your text will flow from one physical piece of paper to the next. Whenever you change paper size in the page setup dialog that representation will change. It will however not change anything of your long flow of text.

This should make it clear why you cannot "delete a page" or "move a page to a different place" as pages do not really exist in this context. Something like "this page" will not be "this page" when you change the paper size. Also inserting or deleting text anywhere in the flow will just move parts of the flow "down" or "up" in the flow, but has no effect on anything "paper page". The resulting flow is simply printed and in some places it happens that the current piece of paper is fully used up and the printer continues on another sheet. The document window simply gives you a visual clue as to where such page break will happen given the current size of paper in the printer.

There are several ways to have (some limited) control over pagination. You can insert a page break anywhere in your flow of text. This is just a signal to the printer to stop printing on the current sheet of physical paper, leave the rest of the paper blank and continue on the next piece of paper. Again depending on the page setup the remaining whitespace on the previous sheet of paper will be larger or smaller. And again the document will try to reflect this by giving a visual clue how things might look when printing.

So the question "What is a page" is kind of moot and makes not too much sense here.

What is a Section?

Still think of your loooong flow of text. You might want to break that flow up into parts. Think "chapter". Each such chapter is called a section. Sections do not change anything regarding the textflow laid out on the printing paper. However sections break your flow into chunks giving a bit more control over how the text should be laid out on the paper. You can have sections start on a new sheet or not, and sections can have individual settings regarding header and footer. Header and footer are independent of your flow of text and are automatically printed on top or on the bottom of any physical sheet, no matter what the text flow. Again the document window tries to give you a visual clue of how header, footer, and your text flow will be mapped onto the sheets. 

Sections have one more advantage. As a section creates a chapter it defines a contiguous chunk of your text flow. This is visually reflected by the yellow border grouping around the "pages" representation in the sidebar. You can move such a section around in your document. This will move parts of your text flow, it does not really move "pages" as those are just a visual clue to how things will be put on paper eventually.

What is a "Layout Document"?

In a layout document you do not have a (possibly very long) flow of text but you work with individual single sheets of paper. Again the print setup dialog defines the dimensions of the paper. In this mode your document does not have a text flow (called the body). You position textboxes and images and whatever on the representation of the printed sheet. If you change the page size things might vanish because they are now (partially) outside the printing area. In this mode the individual "pages" are shown as sections. So each section maps exactly to one physical sheet of paper. This allows you to rearrange your "pages" freely because you can rearrange sections!

Sorry, this was meant to be a reply to the original question, not to you, VikingOSX.