A series of questions about outlook calendar company settings

#1 is easily addressed by creating an "All staff" group, be it "traditional" distribution group, dynamic one or "modern" Office 365 one. The one you have created is local to your mailbox, and while it can be shared out, it's not the best experience. Instead, DGs/Groups are created at the tenant level and are visible to all users by default (you can hide them if needed). You can also apply restrictions as to who can send messages to such a group, or enable moderation, etc.
Here's an example on how to use Dynamic rule: https://learn.microsoft.com/en-us/azure/active-directory/enterprise-users/groups-dynamic-membership#create-an-all-users-rule

#2 is a bit tricker, as there is no "best" solution for the "company-wide" calendar scenario. You can for example combine it with #1 by using a (dynamic) Office 365 Group, which features a Calendar as well, and populate the events/birthdays therein. Or have the Calendar reside in someone's personal mailbox, then share it out. Or use a SharePoint-base done. Each method has its pros and cons, no universal solution sadly.

#3 can be addressed by periodically running a PowerShell script. Unfortunately there is no single setting you can toggle and you will have to rerun this every time a new user is added. But it's fairly easy:

$calendars = Get-Mailbox -RecipientTypeDetails UserMailbox | Get-MailboxFolderStatistics -FolderScope Calendar | ? {$_.FolderType -eq "Calendar"} | select @{n="Identity"; e={$_.Identity.ToString().Replace("\",":\")}}

$calendars | % {Set-MailboxFolderPermission -Identity $_.Identity -User Default -AccessRights LimitedDetails}