If I go to the twitter page of someone I'm following, and click one some of their tweets, on the right column I can see responses. However, when I click on some of their tweets, I don't see responses, I just see other tweets that they made and how many people retweeted that tweet. Does that mean that there were no responses to these tweets?
Yes, it could either be that particular tweet is not part of a conversation (i.e No one replied to it or the tweet itself isn't a reply) or it maybe part of a conversation but the other person has protected their tweets.
Protecting your Tweets
To protect your tweets Log in to Twitter and navigate to your Settings. Then scroll down and tick the check box
Protect my tweets
Save to confirm your changes.