The r at the end of säljer forms a retroflex sound together with the s in sin when they meet.

Here's another one: why is hund pronounced "hmm" here? I listened to it ten times and, with no context, couldn't guess hund.

"Sin" is the possessive pronoun used for the third person singular or plural when the object is owned by the subject, regardless of the gender or number of the subject. In English that would mean "his/her/its/their own". Since in Swedish they have this specific pronoun, if you use "hennes" that would mean that she is selling someone else's dog (some other woman's dog).

I suggest you read the Tips and Notes before you do the lessons. They are very enlightening.

sin always points back to the subject of the sentence. Since the subject is she, it must be her dog. It's her own dog.