How can I pass a char array as the parameter to a function?
There are one or two things missing in your code. Where is setup() and loop()? Or is it just a snippet?

But answer to the question first. This is not right:

newVar = adjust(String(options4[option%4]), variable);


Should be:

newVar = adjust(options4[option%4], variable);


You want to index the vector of strings and pass one of the elements to the function.

Cheers!