What is Office 365 Education for Students? 
Office 365 Education for Students is a combination of two offerings.  First, it provides a cloud-based environment managed by CCPS
where students can edit, store, and collaborate on instructional files.  It provides 1 TB of OneDrive storage, Office Online, and SharePoint sites.  The second offering is the Student Advantage Program that is available for free to students who attend Carroll County Public Schools.  This plan allows students to install Word, Excel, PowerPoint, Outlook, OneNote, Publisher, and Access on up to 5 PCs or Macs and Office apps on other mobile devices including Android, iPad, and Windows tablets.
How long can students use this plan for? 
If you are eligible, you can use the plan until you graduate or are no longer enrolled at a CCPS school.  At expiration, the Office applications enter a reduced-functionality mode, which means documents can be viewed but it isn't possible to edit or create new documents.  In addition, online services associated with the CCPS email address, for example Office Online and OneDrive, will be deleted along with the deactivation of the mail account. 
What is the benefit for teachers and staff? 
This ensures that teachers are using the latest versions of Office and the same feature set as their students.  It will allow teachers to install full Office on up to 5 PCs or MACs and unlock the editing capabilities of the Office apps for iPad.  It also gives them access to all their Office documents both at school and at home.  With Office 365 teachers can take advantage of great Office apps.
What is the difference between Office 365 and Microsoft Student Advantage?
Office 365 is a service provided by CCPS and controlled by an agreement between CCPS and Microsoft.  The Microsoft Student Advantage Program (that allows up to 5 copies of Microsoft Office 2013/2016 Professional Plus to be downloaded to personal devices) is voluntary and an agreement between Microsoft and each user.  It is no different than accepting a license agreement if you were to purchase Microsoft Office yourself.  The only difference is that it is provided free as a result of being a student in CCPS.
How is Office 365 different than storage of files on the internal CCPS network storage?
As a general rule, all conditions that exist related to storage of student files on the CCPS internal network storage apply to Office 365.
Students maintain ownership of their original work through CCPS ownership of the storage medium.  Office 365 is an agreement between Microsoft and CCPS and is an extension of the CCPS technology environment. The terms and conditions of use are NOT between the student/parent and Microsoft.  This is something that differentiates this CCPS-approved service apart from other cloud-based services. The terms and conditions have been vetted and approved as acceptable for CCPS by meeting all data privacy, security, and ownership standards.
Who has access to students' files created and stored in the cloud (Office 365 One Drive) or otherwise created with the provided software? 
Access on Office 365 is setup similar to files in the students' Home Drives on the local CCPS network.  Only the students have access to their own work with two exceptions. First, teachers have secured access to their students’ passwords for the purpose of helping those that forget or lose their password.  Second, Technology Services has access to all storage for administrative purposes (as network administrators).  The key difference to Office 365 is that it provides the capability to enable students to share their files and/or folders with other users within CCPS including students and staff.
Who owns the data, files, etc. produced using the software or online tools?
Students maintain ownership of their original work through CCPS ownership of the storage medium.  This, too, is setup in the same manner as the internal CCPS network storage.  CPPS owns all data stored in the Office 365 cloud.  Unlike some other providers of cloud-based service, the Microsoft terms of use protects CCPS and student ownership of their data. Anything created though a downloaded copy of Microsoft Office is personally owned by the user and not stored in CCPS storage unless elected by the student.
Do the files persist across the school years or are they deleted at the end of each school year?
Files persist as long as the student is enrolled in Carroll County Public Schools.  All students are encouraged to backup their information to a local storage device if they choose.  As is the case with the CCPS network storage, there are no assurances that files cannot be inadvertently lost.  While data is routinely backed up as part of the 90 day retention policy, we cannot guarantee that files can be successfully retrieved and it is the responsibility of each user to backup their own data.  Graduating students should be encouraged to download their information to a local computer if they choose.  During the summer rollover process, graduating students’ accounts and information with be removed.  A daily check it performed to remove all students and their created data that leave the system.
Beyond those which exist when purchasing this software and online access directly from Microsoft, are there any other additional terms of use, agreements, limitations, etc. students/parents are agreeing to by using this software using a school issued ID/account?
No.  More details are provided in other answers.
Will installation or use of these tools on personal computers, tablets, etc. expose or provide information to anyone other than the individual student without explicit parental consent (Administrative account/access, tracking of any king, email retention/archiving, etc.), or otherwise provide someone other than the student with access to the device being used?
Office 365 is a cloud-based service for storage and Online Office application use.  Nothing is stored or tracked on the local computer unless the user chooses to copy information from Office 365 to the local computer.  The Student Advantage Program that allows the installation of up to 5 copies of Microsoft Office 2013/2016 Professional Plus on personal devices is separate program from Office 365.  It is a program that Microsoft provides to students enrolled in participating K12 Systems (which CCPS is).  However, it is not a requirement and strictly a personal choice. The terms and conditions are between Microsoft and the user.  It is no different than if you purchased Microsoft Office for your personal use.  CCPS has no access to anything created on personal devices with the full Microsoft Office download. 
If I download the free Office Apps (like Word and Excel) that are available in the Android Play Store or Apple iTunes Store, does that count as one of my five Student Advantage downloads?
No.  These free versions are "light" versions of the Office Applications designed specifically for mobile devices.  The Student Advantage program provides five free downloads of the full Microsoft Office Professional Plus Suite including full versions of Word, Excel, Outlook, PowerPoint, Access, OneNote, Publisher, Skype for Business, and InfoPath.