Sorry i may take your few minutes, Here are my views on how to increase followers/engagement and reach on twitter.
Hope it helps.
1. How to increase followers?
If your profile is new, you have to follow people from you niche. On a daily basis you should follow 50 to 100 people(relevant to your niche).
You have to do Follow-Unfollow activity from your profile. Consider you are following 50 people today, not all the 50 will follow you back. Give them a weeks time and unfollow those who are not following you.
You Bio should be really interesting and update your picture on you dp and have a interesting cover pic so that your profile looks credible.
You have to update 10 to 15 tweets (informative, humor, engaging and field related updates)
Think yourself as a brand, have a hashtag for you(your brand) and start posting tweets with that hashtag. On a long run you tend to get visibility and you become the source to get niche related information.
Place twitter follow button on your blog. Make sure your content is shareable. Reach out to influencer and share their content on your feed.
Always be an informer to get more followers on any social platform.
2. How to get engagement and reach?
To get engagement on your post, you should tag relevant people on your tweet to get their attention.
Start sharing others content on a regular basis to get engagement in turn.
To create engagement, start sharing others post with your own status message by tagging their profile. (Commenting on someone else's tweet)
Start tweeting happily