The first sentence it's better to say :

انا مع صديقى القط or انا مع القط صديقى....Here you define that you are with your own cat and you are friends.

If you say :

انا مع قط صديقى...it probably means that you are with any cat (like your friend's cat ) and you are friends.

The last sentence you should say :

هو قطى المفضل...make stress on letter (ط)

"I am with my friend's cat"

in this case you should say :

انا مع قط صديقتى...if your friend is female.

انا مع قط صديقى...if your friend is male. Note : also means as i mentioned before, unless you define it more by adding your friend's name.

Hope i get to you what you really wanted to know :)

My pleasure to help :)

Describing the photo

(".انا كنت خطأ. اسمه "

انا كنت مع قط صديقي

هو قطي المفضل