OK. First of all, you’re not being asked to log in because you’ve already logged in previously. That’s nothing to worry about.
Your character’s name is “Alexis”. You can see that in the left-hand bar in the screenshot you posted. You must have typed in that name when you first visited your world, and were invited to create a character - which might have been some time ago.
Your character’s name is different from your account name (fairyhedgehog) because you might choose to role-play different characters in different worlds. For example, if you chose to play Fallen London as a man but Carousel as a woman, then you might want to choose a male-sounding name for one and a female-sounding name for another.
When you use “Godlike Powers” to give a quality to a player, it’s the character name you need to type, not the account name. So in this case, the answer to the question you asked is to give the character “Alexis” the quality “a Stranger”, with value 1.
Note that your character Alexis would have had the quality “a Stranger”, with value 1, when it was first created. At some point in the past, I’m guessing, you’ve already played a branch which removed the quality “a Stranger”, and that’s why you don’t have it any more.
A couple of additional notes…
It’s worth pointing out that I’ve just created my own character (which does indeed have “a Stranger” at 1), and I don’t see any cards at all. So there’s something that’s not quite right there. Take a look and make sure that you have at least one card available which doesn’t require any qualities except for, optionally, “a Stranger”.
Also, I can’t see exactly why the branches on the card in the screenshot are locked, but you might want to take a look at the way it’s designed. If they are locked because they all require “a Stranger 1”, then it might be a better idea to place that requirement on the card as a whole - up at the top, in the section titled “Root event” - and not on each of the individual branches. Setting it on both the root event and the branches might seem like a sensible “belt and braces” approach, but it’s not really necessary, and it’ll cause strange and confusing problems if you make a mistake doing it.
Hope that helps! Do post again if this doesn’t solve it… I’m going to be on a plane tomorrow so I might not be around myself, but I’m sure someone else would pick up.
Cheers
Richard