relay-starter-kit | Barebones starting point for a Relay application | GraphQL library

It's very difficult to solve the problem with the information provided in question. As you requested guidance, here's my suggestions :)

I cant understand why its populating the search fields the first time but not on typing in the search form.

Because Relay fetches the result for the initial value of searchTerm, which is an empty string in your case. You have to deal with this case on the server side (by checking the input searchTerm) and client side (by checking if the current value of searchTerm is empty, for example).

When you type in search form, search() isn't called and searchTerm is not updated. Check SearchForm component.

When I use the search form, I get an error in the browser saying "app.js:8284 Uncaught TypeError: Cannot read property 'edges' of undefined".

Start debugging what the server side returns for quotes field under viewer GraphQL object type. What's the output of db.collection('quotes').find(findParams).toArray() in your schema? In addition, put a console.log(JSON.stringify(this.props, null, 4)) in render() function of App class. Check what you see. You can also inspect the HTTP request and response on the Chrome DevTools Network tab. Filter by graphql.