"You're welcome! Goodbye!"
Bu and keqi are the two different words here. You see often in chinese that two characters together make one word.
What does this literally translate to? I'm guessing some variation of "No problem"?
'No need for the civility, see you again' This is more or less the literal translation. The first part however can be seen as no problem or you're welcome, this is more of cultural reasons.
Not in this context, 欢迎 is like a "warm reception"; "welcome aboard" The English here seems to be a response to someone's "thanks".
As far as I know, 欢迎 is used when you greet someone (welcome), and can't be used as a polite answer to 'thank you' (you're welcome). Correct me if I'm wrong :)
Usually "you're" is implied so it is "欢迎！" As a response to "Thank you", it is incorrect, as @Celticfiddleguy and @Lomochibi pointed out.
There is nothing in the hints to suggest this answer when you have the English and the characters to drag in - I am sure they are correct word by word but if the words don't translate to the phrase it makes it difficult to learn from.
The sound is missing for 不客气, This was posted a year ago and is STILL not fixed? Yet they have time to do an unneeded redesign of the app? Bah.. doulingo is losing points with me.
To be fair, in the context of your points being very valid, the new tips and notes section, available on mobile now, is an improvement.