Here are some commands that are handy to use for Office 365.

#Assign user credentials to variable "LiveCred"

$LiveCred = Get-Credential

#Connect to your Cloud-hosted Exchange using the credential stored in #LiveCred

$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection

#Import Cmdlets

Import-PSSession $Session

#Close your session

Remove-PSSession $Session

#Grant Bob Barker calendar (or any folder) rights to Adam Sandler's. The field within " " can be either the user principal name or primary alias
#Possible   rights:  Ownder, Publishing Editor, Editor, Author, Contributor, Reviewer, Custom
#Note: practice-wise (for your own mental check), the account being given access is normally to the right of the account to which you are assigning the right.

Add-MailboxFolderPermission -Identity "The.Dude:\Calendar" -AccessRights PublishingEditor -User "Test Guy"

#View permissions on a folder

Get-MailboxFolderPermission -Identity "The Dude:\Calendar"

#View all accounts that have mailbox access beyond SELF

Get-Mailbox | Get-MailboxPermission | where {$_.user.tostring() -ne "NT AUTHORITY\SELF" -and $_.IsInherited -eq $false}

#The export to a file version of above

Get-Mailbox | Get-MailboxPermission | where {$_.user.tostring() -ne "NT AUTHORITY\SELF" -and $_.IsInherited -eq $false} | Select Identity,User,@{Name='Access Rights';Expression={[string]::join(', ', $_.AccessRights)}} | Export-Csv -NoTypeInformation mailboxpermissions.csv

#Grant user Send-as to identity

Add-RecipientPermission <identity> -AccessRights SendAs -Trustee <user>

#View all boxes that have Send-as attributes on them

Get-RecipientPermission | where {($_.Trustee -ne 'nt authority\self') -and ($_.Trustee -ne 'null sid')}