Twitter accounts I follow not appearing

This is part of the Twitter experience.

Your home timeline, the page you see when you log in, will contain tweets from your own account along with all of those you are following and other tweets that have been retweeted (if you haven't turned that off).

This is found here:

https://twitter.com/

When you view a profile's timeline you only see tweets from them and their retweets. You'll know you're on a profile timeline when the URL is like:

https://twitter.com/{username}

How they keep up depends on how they use it and various apps they might use with Twitter.

Some people follow thousands but don't really check their timeline and only look at any mentions toward them. Others might create a list or two with a few tweeters and only check that, cutting down on the noise.

There are two answers to this:

Public Account

Yes. All they have to do is go to your page https://twitter.com/yourtwittername and they can see what you tweet.

Private Account

No. If they go to your page https://twitter.com/yourtwittername all they will see is your name, bio, and link.

If they then try to follow you, you'll get a notification that someone wants to follow you and you'll have to approve the request before they see your tweets.