Merriam-Webster's Learner's Dictionary
vice versa
— used to say that the opposite of a statement is also true
▪
She ended up having a lot of influence on his career, and
vice versa. [=and he also ended up having a lot of influence on her career]
I believe this is a confusing, but common, misuse of vice versa. 'He' and 'her career' are not even mentioned in the original sentence, so they can't be the elements. The vice versa is "His career ended up having a lot of influence on her."
"She likes my dog."
The vice versa is "My dog likes her", not "I like her dog."
▪ The camera can adjust for a light subject on a dark background, or
vice versa. [=or a dark subject on a light background]
That sounds right.
Merriam-Webster's Learner's Dictionary
conversely
formal : in a way that is the opposite of something else
▪ Large objects appear to be closer. Conversely, small objects seem farther away.
Do you say "conversely" instead of "vice versa"?
Generally not. It's not colloquial. However, you could use it for the above sentences.
She likes my dog, and conversely, I like her dog.