No. Bug Tracker is not available as part of our free plan. You need to upgrade to a paid plan. For more details see Plans and Pricing.
Note: In addition, you can also take a look to know the benefits of the new Bug Tracking.
Business Rule is a kind of filter that you will apply to all your bugs. You can define Business Rules that will enable you to organize the bugs and perform action such as changing the severity, status, module, classification and assigning the bug to a user. Business Rule will be triggered when the bug is created and whenever there is an update in that bug.
For example, When a particular bug classification is feature request/ enhancement, then "is it reproducible" has to be updated to Not Applicable there. This can be defined as follows

Now, Whenever a bug classification is updated to "Feature(New)" or "Enhancement", "Is it Reproducible" will be updated to " Not Applicable ".
In a similar way, you can configure your own set of business rule as per your project needs.
Yes. The portal administrator is the only person who can create a module for your bug tracking module.
To create a module :

In addition, we've provided options to edit / delete your modules.
Each issue has a status, which indicates the development stage of the issue. The following are the default statuses
You can modify the statuses as per your requirement. If you want to change the default status, Click the edit link corresponding to the status for which you want to set as a default one. Also you can add your own statuses using "Add Status" link present at the bottom. In addition, you can order it to your own choice using the drag and drop option. Furtheremore, you can delete the existing statuses (Default status can not be deleted).

Yes. You can associate a bug to an existing milestone when submitting an issue. The following screen capture explains how to associate an bug with a milestone.

Yes. My Bugs view provides a consolidated view of bugs filed by you or assigned to you for a project.

Yes. The client user will be able to change the status only when he/she is assigned to the bug.
To assign the bug to the client user, two conditions must be met.
1. The Assign external bugs to client users option must be enabled: Once you are in the Bugs module, click Bug Settings --> Client Permission menu and enable this option.
2. The bug's flag must be external: You will be able to see the list of client users while filing the bug only when External flag option is opted.
Currently it is not possible to associate a bug to a task. A bug can only be associated with a milestone.