I'm a bit confused. Björnen is pronounced with the 'o'-sound from (for example) the English word "come". I thought the 'ö' always was pronounced as 'u' as in "fur", so I thought 'Björnen' would sound like 'Bjurnen'.
Why isn't is just 'Bjornen' than, because (as a beginner) I would think that's the same.
In Swedish, except for the southern dialects and the Finnish dialects, the combination -rn-, merge into a thicker ”retroflex” sound. If it were just ”bjönen” then the -n- would have been more dental. What you have to do is just move the tip of the tongue a bit further back in the mouth when producing -rn-. Same goes for -rd-, -rt-, -rs- and to some extent -rl-.
No, in British English the /r/ disappears altogether. In this case, it just merges with the /n/, /d/, /t/ and /s/ to form a sound where the tongue is more bent backwards.
Listen to the difference between: ”bord” and ”bod”.
And between ”höna” and ”hörna”.