Nope no need to root sir.
Here this will solve all you problems:
1st issue: change web browser at bottom to dolphin.
- Open up your applications drawer, hit menu button and select view type. Select customizable grid. Once you are in that grid, scroll around your app drawer and find dolphin...hit menu...hit edit...long press on dolphin app, slide to your dock at the bottom where you want to place it. Once its done just press the home button on your phone...should have replaced dolphin with the default web app there.
2nd issue: default email to gmail???
- can you be more specific? like do you want the email app to show your gmail ...? Just answer this question: How is gmail not your default email?
Hope i helped and feel free to give thanks below.