Hi @Liz Day!
The (non-exhaustive) list of core Miro integrations can be found here.

Of them, the following are not available on the Education plan:
Jira Cards, Asana Cards, Azure Cards, Rally Cards, Jira add-on
Most other integrations and apps should be available.

To answer, your questions about Asana and Box:

• You can attach Miro boards to Asana tasks or project briefs on the Asana end regardless of the plan the the team where the board is located is on. However, importing Asana tasks as cards onto a Miro board is only available on paid plans.
• The Box integration can be installed on any plan.

Hope this helps!