The issue is that Outlook need someplace to store the local items, such as your Tasks, your Calendars, Notes, etc. With IMAP mail servers, your mail lives on the IMAP server, and it can have it's own folder structure aside from the local folder structure. This is why you see both 'trees'. When you use Outlook with POP3 mail servers, POP3 functions differently; the mail is downloaded from the POP3 server and then stored in your local mail folders (and then usually deleted from the POP3 server). So you only ever see one 'tree'.
You mention that with Exchange you don't see the 'Outlook Data File', that's because Outlook works with the exchange server directly, and the Exchange server is your 'Outlook Data File'. That is, the Exchange server is the storage location for all our email, tasks, notes, calendar, etc. If you then add an IMAP account, you should see both the Exchange Mailbox and the IMAP folder structure similarly.
To answer your questions directly: I'm not sure if you can set whether various panes are hidden or shown by default; you might be able to accomplish this via Group Policies but I'm not sure. I suspect you would need to go to the individual machines and just do these things and then it will remember how you have things arranged. You can however remove the Data File version of 'Inbox' and other folders from the favorites and instead add the IMAP versions (they will look different though).
Regarding the Junk-Mail settings, there's a difference when you're using Exchange server. Exchange server itself is [generally] capable of handling junk mail, and it can scan and move mail into the junk mail folder without the intervention of Outlook. This is different than an IMAP server, again keeping in mind that your mail lives on the IMAP server, Outlook is not actively monitoring incoming mail for you. Instead, when you connect to the IMAP server, the IMAP server tells Outlook what mail is there waiting to be read. For the most part you would need to have some server side junk mail filtering going on to effectively deal with the junk.
I hope that helps, even though its probably not the answers you wanted.
I finally found an acceptable way to deal with this Gmail/Outlook 2013 issue.
Go into your Gmail settings at gmail.com. Under When I mark a message in IMAP as deleted set Auto-Expunge to off. Then set When a message is marked as deleted... to Move the message to the Trash (or something else, if you prefer). Click Save Changes.
In Outlook 2013, click on your Gmail inbox. Then, at the very top of Outlook, click on Folder. You'll see Purge in the toolbar area in the middle. Click Purge then click Purge Options. Select the Advanced tab. Uncheck both checkboxes under Delete Items. Click Ok. (Note that checking the option "Purge items when switching folders while online" doesn't seem to have any effect with this setup.)
Now when you receive and then delete a new email in Outlook, Gmail will put that email in your Trash folder. Gmail also gives that email the Trash tag, but it does not remove the Inbox tag.
This isn't 100% ideal, as the Inbox tag remains on the email. However, since it does receive the Trash tag and ends up in your trash (and does not appear in your Inbox nor in All Mail) this is acceptable to me. Gmail deletes all items in the Trash folder when those items are 30 days old. I also cross checked this with my phone (an iPhone). From what I can tell, everything behaves as I would expect.
Best Answer
It seems something in your outlook profile has gone corrupt. You should do the following:
Now try again. If all works, and you don't need your old profile anymore, you can remove the profile.