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Your professor deceived you :)
You can say either "Ja kazhdy den zapominaju novoe slovo" or "ja uchu po odnomu novomu slovu kazhdy den".

Запоминать = memorize, commit to memory (and not "recall"...

Yes.
Признать = acknowledge, admit, recognize, accept.
But, of course, everything depends on the context. In your context (the sentence "You've got to admit that British Peoples' accents are...

Pronounciation: Dah-poosk-at'/Dah-poost-it'


Actually, in Russian it would be something like this:
Вы должны признать, что британский акцент обаятелен/притягателен/приятен.