Firstly i am going to explain what i am trying to do. I am trying to create an app in which the user can create or remove existing database fields.

There will be a drag and drop form builder that will manage each of the form fields in existing tables.

More over the user can also create new tables from the front end. For example, there may existing tables like books, class timetable and the user may want to create a new form/table which would be called tasks. After this, the user can create form fields in this newly create form/table.

I have drawn out some plans on how to do this but i am looking for better suggestions out there. I am really confused on whether to create new tables for each new custom feature the user wants to add.

A typical example of this kind of app is zoho crm. You can check through the screenshots.

My major questions are

How to structure the database for this
How to create the drag and drop form builder that will save the new fields and update existing fields on the database.

Most times, the basic idea you need to know to build standard web applications is what I like to call "Normalization".
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Think about every possible database table you'll need in your application and write them down. Now, for each table, make a rough drawing, indicating all the fields (columns) you'll like to have in it. You can do this using any word processor like MS-WORD.
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After that, try to see if you'll find similarities between tables. If two or more tables seem to have similar fields, then you're heading to get something done the wrong way. On the other hand, if there are no similar fields appearing in multiple tables, then you're getting it right!
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The main point here is to assign unique content to separate tables. For example, let's say we have three tables:
1. teachers
2. students
3. subjects
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Different teachers may teach different subjects in a school. And students may also have different subjects. So, it's okay for me to create each table separately.
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Hope it helps.