GMail handles mail in ways like no other services, to be frank, and you are not alone in finding some of its oddities confusing.
Most other apps for mail keep messages in single folders, while GMail is intended to keep a single copy of the message and then show it with any different labels you have attached to it.
To remove something from the Inbox you need to "Archive" it, so it is no longer shown when viewing your Inbox. Messages are always shown in "All" unless they are classed as Spam by Google and get shown only under that label.
Sorry, I do not use Outlook (I assume you mean either the Outlook 365 app or Outlook 2016 on Windows 10) but...
to the point of your question, I doubt you can create a new label unless you use GMail from a web browser.
I cannot create a new label when using the GMail app on iPhone, Android v7.1.1 or Android v4.3 (the phones I had to hand).
Originally, GMail was probably used most from a desktop / laptop, so I assume they considered it too awkward from a mobile to create new labels, and given the label system is 'peculiar to GMail' and not udentical to folders on an IMAP server, so Outlook will be unlikely to have the ability.
Going on to your wish for Pending, Complete and Archive, might I suggest you name your labels "MyPending" "MyComplete" and "MyArchive" in part because one or more might clash with the way GMail uses the names in future, and because the GMail "archive" is really just removal from Inbox and the only way to see them would be to display All (which would show everything, where you want to keep your pending, complete and archive categories distinct.
Best of luck - I hope what I've picked up over the years helps.
PS Just looked at my first message - subject "GMail is different..."
(dated 8 Jun 2005, 18:47) It was on page 904 of my messages, message number 90421.