How do you install SQL Server Management Studio (SSMS) v 18.4?

Since SQL Server 2016, SQL Server Management is not installed when you install SQL Server. It will be a separate install.

You can download the latest SQL Server Management Studio v18.4 (the most recent version) from here:
https://docs.microsoft.com/en-us/sql/ssms/download-sql-server-management-studio-ssms?view=sql-server-ver15

It is backward compatible with the earlier versions.

Double click the downloaded file (SQL2019-SSEI-Dev.exe) to begin the installation.

 Click Install. It takes a little while and gets installed easily.

 You should see this in your Windows Display of programs.

These programs get added to your Control Panel.

When you launch the SQL Server Management Studio you may get this display. Since there was an existing SSMS v 17.x was present, this display came up. 

The user settings from v17 were imported. You could also import later after a default installation.

The SQL Server Management Studio opens displaying the Object Browser. It assumes Windows Authentication with the current user as server administrator.

The version information is as seen in the following screen:

What is the PowerShell cmdlet version that works with (compatible) SQL Server 2019?

PowerShell is in continuous development mode. New challenges require updating of software to accommodate the changes. This is the nature of such things. PowerShell cmdlets also follow this natural course and we have many versions.

I had an older version, and when I tried to launch contextually from SSMS v 8.4, I got this response:

In order to get the version you want, you may access this link:

SQL Server with PowerShell

Here is a list from the above site:

What happened to the Query Debugger icon in SQL Server Management Studio v 18.4?

It looks like it has been deprecated in SSMS 18. I have SSMS v 18.4 installed and the icon is missing. Also missing is the Execute with Debugger drop-down menu in the query pane context.

Debug icon present in 2012 and 2017 SSMS. Missing in v18.4 in the 2019 version.

Missing in the Query drop-down menu. It should have been present below 'Execute'.

What are the scripting options in SQL Server 2019?

What are the scripting options in SQL Server 2019?
The Scripting options can be accessed from Tools: Options in the SQL Server Management Studio v18.4.

In the Options window drill-down on SQL Server Object Explorer | Scripting as shown.

 Expand the node, General scripting options to display the following:

 Expand the node, Object scripting options to display the following:

 Expand the node, Table and view options to display the following:

 Expand the node, Version options to display the following:

In each version of SSMS, the Options window is slightly different or arranged differently.

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What is XEvent Profiler in SQL Server Management Studio (SSMS) 2019 and where do you find it?

XEvent Profier's role in SSMS is for troubleshooting SQL Server Issues such as slow running queries, identify long-running queries, monitor SQL statements, etc. From Version SQL Server 7.0, SQL Profiler was used, but it was not easy to use due to the lack of a GUI.

SQL Profiler was replaced by XEvent Profiler which is easy to use and presents a quick view of Extended Events.
XEvents is a feature of SSMS and not SQL Server and it was available in SSMS V17.3.

It is also available in SSMS V18.4 which is the latest version of SSMS as of now. You can find in the Object Explorer (bottom-most node)  of SSMS as shown here.