Is it okay not to put "together" or "with" after "click"? Or both "click" and "click with/together" okay?
Yes! It is totally fine to just have the word "click" without "together" or "with." The word "click," as you may already know, has a few meanings. In this scenario, it means to get along really well with someone when first meeting; to have things in common with a person that you first met. Ex: The two of them clicked right away. Ex: I think Mary and Jack will click once they meet.