Great to see Microsoft has enabled Planner Preview for all applicable tenants. This has created a huge speculation among Office 365 users and the long wait has come to an end by this.

Now as I see in the forums many of the planner lovers has questions that they are looking for answers. Below are the some of the FAQ's I have noticed in discussions.

For introduction about Office365 Planner with screenshots, refer this blog Office 365 Planner for Visually Organizing Team Tasks

Yes, the global admin need to set your full tenant for First Release. Once this is done, Microsoft will find yours as the eligible tenant for preview and then you can able to see instructions to enable and assign licenses to users from Admin Message Centre. For more details check Step1 in the article.

It is based on the choice of the Admin to assign the licenses to users. Only the license applied users can able to see the Planner in their App Launcher. For more details check Step2 in the article on how to assign licenses.

Definitely not. If an user creates Office365 Group first then the Naming policy is applied to this group and the same name will be used as the plan name. If the Office365 Group was provisioned by creating a  Plan first, then this naming policy will not apply. This feature is listed in Microsoft roadmap.

Yes, the Documents put in the library via someone attaching to a task can be accessed by the user (non Planner licensed user) in the Office365 Group via One Drive or from Files menu in group.

Yes, but those APIs are in beta now. APIs are available for Tasks, Task details, Plan details, Buckets. Actions like Get, Create, Update and Delete can be performed using these APIs.
http://graph.microsoft.io/docs/api-reference/beta/resources/task

No, as of now. But as per message from Microsoft, they are rolling out this feature to First Release enable tenants soon. The "Plan" can be accessed from Office365 Groups menu list just like Calendar, Files, Notebook.

Update: 23 May 2016

Yes, currently it is limited to 350 pans per user.

Currently you can able to do this by tagging each tasks with text and colours. It is requested for a new tasks view based on priority and listed on user voice
https://planner.uservoice.com/forums/330525-planner-preview-feedback-forum/suggestions/11629665-i-need-to-be-able-to-prioritise-tasks-so-that-i-ca

Mobile App for Planner
Microsoft is working on Planner app for Android and iOS and will be available as Windows Universal App. May expect availability by end of this CY.

Sync Planner my tasks with Outlook my tasks
No such connector is available as of now to sync this. We (JiJi Technologies) are working on an Outlook app named Apps 4 Pro that will sync these and helps you to manage planner from outlook itself.

Office 365 Groups and Planner relationship
Currently Groups and Planner have 1:1 relationship. That is for each Plan a Group is created. Users expected to have one group for many plans.

Move tasks between plans
Organizations with huge plans have a need to move a task from one plan to another. This feature is available in Apps 4 Pro planner as an outlook add-in.

• Template / Clone for Plans and Tasks
• Search tasks / plans
• Email notifications customization
• Prioritize tasks based on importance
• Delve search indexes planner documents

You can use Rest APIs for this which are in preview now.
For Tasks management: http://graph.microsoft.io/en-us/docs/api-reference/beta/resources/task
For Plans management: http://graph.microsoft.io/en-us/docs/api-reference/beta/resources/plan