Why is it friend sing. and not friends pl.?
I presumed that "...aapNE dost ke..." Insinuated that dost/friend was plural.
I have the same question. You use aapne because using postposition ke saath makes you use oblique, but anyway I questioned if first could be plural
In the "select the missing word" exercise, couldn't it be also अपनी if he was with a female friend?
Yes. अपनी is also correct with the assumption of female friend.