Hi Hieu 
The details that you see for each merchant come from several sources. First, Monzo will try to match the information that they get about a transaction against the Foursquare, Google Maps etc. databases to retrieve the rich company details. If that doesn’t work, users can correct the data themselves (there’s a dedicated button on iOS & you can send details to the support team, using the chat tool on Android) 
https://monzo.com/blog/2016/04/11/crowdsourcing-merchant-data/
As you say, once you’ve registered for an account, swiping left with three fingers on the screen that’s showing your place in the queue, is the way to activate your card immediately. If that doesn’t work, you’ll need to contact the support team by emailing help@monzo.com or sending them a DM on Twitter.
To clarify, your friend’s card won’t be linked to their account, unless they linked in themselves & activating the card this way isn’t against the T’s & C’s.
PS - once you have linked your card to the account in the app, it would be great to hear your user number (from your profile) for this -
https://community.monzo.com/t/number-of-monzo-users/4196/174?u=alexs
