@Somanysocks
You should be able to click on a twitter link and see a tweet.
Twitter may ask you to join or download the app, just reject that option and you shold see the linked tweet.
You need to click on the show reply option to see additional direct replies.
Or if you can see a direct reply click into the reply tweet and then its show reply to see all the tweets is a conversation thread.
The more tweets section are not directly related to the original tweet they will ususlly have a common topic.
If you scroll down into the first one Twitter will push a block screen (show whats happening /join). You need to refresh your address bar to get rid of that screen.
If you quickly scroll passed the first one twitter will let you see the others.
You can also click on the individuals name and scroll down their time line to find a tweet. Again after about 5 tweets, twitter puts in a topic break that you have to quickly scroll past skipping 1 tweet to see older ones.