See explanation below.
Explanation
* In the EAC, navigate to Mail flow +. This starts the New Send
connector wizard.
* On the first page, enter the following information:
- Name: Enter a descriptive name for the Send connector, for example, Smart host to Internet.
- Type: Select a descriptive value. For example,
When you're finished, click Next.
* On the next page, select Route mail through smart hosts, and then click Add +. In the Add smart host dialog box that appears, identify the smart host by using one of the following values:
- IP address: For example, 192.168.3.2.
- Fully qualified domain name (FQDN): For example, securitydevice01.contoso.com. Note that the Exchange source servers for the Send connector must be able to resolve the smart host in DNS by using this FQDN.
When you're finished, click Save.
* You can enter multiple smart hosts by repeating Step 3. When you're finished, click Next.
* On the next page, in the Route mail through smart hosts section, select the authentication method that's required by the smart host. Valid values are:
Table Description automatically generated

* When you're finished, click
* On the next page, in the Address space Add domain dialog box that
appears, enter the following information:
- Type: Verify SMTP is entered.
- Fully Qualified Domain Name (FQDN): Enter an asterisk (*) to indicate the Send connector applies to messages addressed to all external domains. Alternatively, you can enter a specific external domain (for example, contoso.com), or a domain and all subdomains (for example, *.contoso.com).
- Cost: Verify 1 is entered. A lower value indicates a more preferred route for the domains you specified.
When you're finished, click Save.
* Back on the previous page, the Scoped send connector setting is important if your organization has Exchange servers installed in multiple Active Directory sites:
- If you don't select Scoped send connector, the connector is usable by all transport servers (Exchange 2013 or later Mailbox servers and Exchange 2010 Hub Transport servers) in the entire Active Directory forest. This is the default value.
- If you select Scoped send connector, the connector is only usable by other transport servers in the same Active Directory site.
When you're finished, click Next.
* On the next page, in the Source server section, click Add +. In the Select a Server dialog box that appears, select one or more Mailbox servers that you want to use to send outbound mail to the smart host. If you have multiple Mailbox servers in your environment, select the ones that can route mail to the smart host. If you have only one Mailbox server, select that one. After you've selected at least one Mailbox server, click Add, click OK, and then click Finish After you create the Send connector, it appears in the Send connector list.
From the Send connector list, you can turn the connector on or off.
Reference:
https://docs.microsoft.com/en-us/exchange/mail-flow/connectors/outbound-smart-host-routing?view=exchserver

Reference:
https://docs.microsoft.com/en-us/exchange/hybrid-deployment-prerequisites#hybrid-deployment-protocolsports-

Reference:
https://docs.microsoft.com/en-us/exchange/permissions-exo/feature-permissions

See explanation below.
Explanation
Use the EAC to create a public folder mailbox
* In the EAC, go to Public folders > Public folder mailboxes, and then click Add +.
* In the New public folder mailbox page that opens, enter the following information:
- Name: Enter the name for the public folder mailbox.
- Organizational unit: Click Browse to select the location in Active Directory where the mailbox object is created.
- Mailbox database: Click Browse to select the mailbox database where the mailbox is created.
When you're finished, click Save.
Use the EAC to create a public folder
When using the EAC to create a public folder, you'll only be able to set the name and the path of the public folder. To configure additional settings, you'll need to edit the public folder after it's created.
* Navigate to Public folders >
* If you want to create this public folder as a child of an existing public folder, click the existing public folder in the list view. If you want to create a top-level public folder, skip this step.
* Click Add +.
* In Public Folder, type the name of the public folder.
* In the Path box, verify the path to the public folder. If this isn't the desired path, click Cancel and follow Step 2 of this procedure.
* Click Save.
* Navigate back to Public folders > Public folders.
* In the list view, select the public folder that you want to mail-enable or mail-disable.
* In the details pane, under Mail settings, click Enable or Disable.
* A warning box displays asking if you're sure you want to enable or disable email for the public folder.
Click Yes to continue.
Reference:
https://docs.microsoft.com/en-us/exchange/collaboration/public-folders/create-public-folder-mailboxes?view=ex
https://docs.microsoft.com/en-us/exchange/collaboration/public-folders/create-public-folders?view=exchserver-2
https://docs.microsoft.com/en-us/exchange/collaboration/public-folders/mail-enable-or-disable?view=exchserver