The easiest first. Getting the users Library visible, again, permanently:
First, change the Finder Preferences, at least temporarily so that the users home icon is displayed in the Side Bar. I don't see your wife's Home icon showing in your screen shot. If she/you don't want to see that in the Side Bar, you can change the prefs back after the instructions below.1. Open a Finder window (in the account you want to end up being her main one, we'll worry about the others, later).
2. In the Go Menu, scroll down to "Go to Folder..." [shift-command-G]
3. In the text box, type /Users/WHATEVER-HER-USER-NAME-IS(it should be the same name showing beside the Home icon)/Library and click the "Go" button.
4. Click and hold the folder icon at the top of the Finder window that opened in step 3.
5. Drag that folder icon into the Side Bar of the other open Finder window.
6. Close the second Finder window that has the contents of the user Library.

Change Finder Prefs

Go to the users Library (~/Library)

Drag the Library icon to the
Finder Side Bar
ISSUE 2: Have you tried the Import Mailboxes... menu item?
As for "What is the V2 folder?" I think you can pretty well se what's in there. Pretty much everything Mail needs to display your messages except the attachment downloads. I think that folder started back in Snow Leopard but I'm not positive. 
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I see 4 POP folders.
Which is the right one? Can I delete the others?
About a year ago our ISP provider changed our mail format. The current one is Pop3.live.com ( I think!)
Don't delete any of them! At least not in that directory. All those folders are created by Mail when you set up the app's preferences. Since you have two nearly identical accounts, you have two of many of those folders/files. You need to get rid of the extraneous account and it's log in before tackling the Mail problem, IMHO.
I've already discussed how to use two windows, one for each user, to transfer stuff between a secondary user to the primary user's Public folder. The "trick" is to be logged IN to the secondary user's account, otherwise, you cannot see what is there to transfer. 
I don't have any Microsoft apps so I have no idea how to install Word. Nor do I have any interest in learning!
BTW, I didn't know Word did "accounting!" Excel (horrors!) maybe, but Word?
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It was installed on the G4 from Install Discs. Of course, the Mac Mini can't read those. How do I install that app?
Showing my ignorance, again, but why can't the mini read/install from those? Does it not have a DVD/CD reader? 
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When I tried to Import that folder, it had a ton of pictures in it... there is a Pictures.mbox, and an iTunes.mbox and videos.mbox. Doesn't look like email to me!
They could simply be pictures, music and movies hat were sent as attachments with some message. When I can get to my grand daughters machine, I'll look at the files/folders/etc in her version of Mail and see if I can determine what's where and why. I think se's still using Snow Leopard if not Leopard, so the setup should be more like yours. Pictures at noon? 
As for the user/Library (~/Library) it does appear that you've got it displaying properly. I got confused with the "All this and not being comfortable with a new OS (Where is the Library folder? etc). " in your original post (#1). My confusion, not yours!
ISSUE #1:QUOTE
The Mac Mini has no DVD reader. How to load MS Office 2008 from the Install CDs?
My first idea would be to re-create then as Disk Images. Assuming you have a DVD reader in something, you can use Disk Utility to create a file that can be loaded onto the mini's HD and used as a 'virtual disk.' That's the way many apps are downloaded from a developers site, for example. You then double-click the file (which will have a ".dmg" suffix) and it 'becomes' a volume/disk with all the MS installer apps on it. Details can be discussed later... I'm about to turn in for the night. 
The "-" symbols: We're still getting confused with which account we're logged in to. The "-" symbol is only on folders that the currently logged in account does not have access to, because they are owned by another account. In order to see/use/access/transfer what's in those folders, one must be logged in to the folders owner account.
Pictures tomorrow!?
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I only have one monitor which is a pain when going from the Mini to the G4.
Well, I may sound like a party-pooper, but she'll never be able to use that thing without a monitor. And things will be much simpler when you have on on it, also. I'm simply suggesting that the first thing to do is to get a monitor. They are relatively inexpensive, doesn't need to be one from Apple, at all. You will probably need a <$30 adaptor to connect the monitor. First you need to find out what the video out on that model is. If it came with 10.7, it must be a couple of years old...