"Her brother is my uncle."
Translation:Hendes bror er min onkel.
Yes, that is the most common way to pronounce a k in Danish, when it is not in the beginning of a stressed syllable or the start letter. It is not considered wrong to pronounce like a k, though.
For instance in 'konkret' and 'kakao' all four k's are pronounced like k's, because both are in the beginning of the word or a stressed syllable. (stresses are on the second syllables)
In 'kirke', the second k is pronounced lige a hard g, while the first is a k. (stress is on the first syllable)
And in 'onkel' and 'ikke' they are pronounced like g's again because stresses are on the first syllables.
"Hende" is her, as in "I love her" = "Jeg elsker hende". "Her" refers to the person that she is
"Hendes" is the possessive pronoun, for example "Jeg elsker hendes kat" = "I love her cat". Here "her" shows that the cat belongs to whoever "her" refers to, but it is not her that "I" love, it's the cat she owns. Think of it like the word "hers", just also used before a noun rather than just on its own.