There is a misunderstand, the feature you asked in Q4), there isn't such kind of built-in feature within message system demo. So you will need to customize the nested view, and style/format the result.
For user "Liluhot", he starts the message, in the message post, the field "Message from" value is "Liluhot" user's ID.
In order to display message posts start by current logged-in user, you will need to add a filter into parent post view:
1) Edit the post view "Messages received - 2":
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Add a filter:
OR
Message from is a string equal to VIEW_PARAM(messagefrom)
2) Edit the page "Inbox 2", change the shortcode as below:
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[wpv-view name="Messages received - 2" messageto="[wpv-user field="ID"]" messagefrom="[wpv-user field="ID"]"]
Login as user "Liluhot", test the problem page again:
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You will be able to see the messages start by user "Liluhot".
And I have setup a content template in post view "Messages received - 2 child":
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1) In section "Ordering ", use option: order by post title ASC
2) in section "Limit and Offset", use option: skip 1 item(it will skip the first message post)
[wpv-post-link] - [wpv-user field='user_firstname' id="[types field='message-from'][/types]"] [wpv-user field='user_lastname' id="[types field='message-from'][/types]"] - <a href="[wpv-post-url]#reply" class="small reply"><i class="fa fa-reply" aria-hidden="true" title="reply"></i></a>
And it is only an demo, you will need to customize/style the result manually.
And in my opinion, you don't need the "outbox" page any more, since above parent post view can outputs all messages "send from" or "Send to" current logged-in user.