As you say:  your .EXE is on the server and NOT on the CLIENT.

Some terminal emulators (e.g. KEA) once had the feature to launch a LOCAL command triggered by an ESC sequence.
But this requires your .EXE to be already installed on your LOCAL client.

You may need to have a telnet or SSH connection to your client.

Browsers typically don't allow this. But they may run JavaScript (which isn't  your .EXE)

It's not really clear what you expect by "ID of the task"

You get the actual process id by system variable  $JOB.

If you look for the Task Name as seen in Taskmanager then  $this.GetTaskName() as %String
Returns the localized name of this task.
see docs of  %SYS.Task.Definition ​​​​​​​

the DEFAULT function of # for a terminal window emulating a CRT ist hardcoded.

see Terminal I/O WRITE

"Issuing WRITE # to a CRT terminal clears the screen and sends the cursor to the home (0,0) position."

using a Mnemonic Definition you may supply the required escape sequence to cover your needs.

but instead of WRITE #  you may need to use  WRITE /TOP  (just as an example)

For all about Mnemonics see Controlling Devices with Mnemonic Spaces.

Zen Application is the "package" you call from a browser and typically sets a common design.
Zen Pages are the individual web pages that make up your application.
Client Methods is JavaScript executed in your browser.
Server Methods run on the Caché Server and interact with the Zen page using HyperEvents.

I'd suggest you take a tour through the docs for details. 

you operate not on document object but on zenPage object

see docs:  Client Side Functions, Variables, and Objects  at the beginning >>>

• Find a Zen component by id value. Returns the object that matches the input id.

• The zen(id) JavaScript function is equivalent to the following client-side JavaScript method call on the page object:

• zenPage.getComponentById(id)

• You can use the zen(id) function wherever JavaScript syntax is appropriate; 

but that way

USER>f a=0.8:.1:2.2  w a,?7,a\1+(a#1>0*1),?10,!
.8     1
.9     1
1      1
1.1    2
1.2    2
1.3    2
1.4    2
1.5    2
1.6    2
1.7    2
1.8    2
1.9    2
2      2
2.1    3
2.2    3

In namespace %SYS you have the utility  ^JRNDUMP  which displays the content of journal files in "readable" text format.
You may need to adapt it to your requirements.

Depending on your activities in the DB  this may take many many GB !
I'd suggest examining the content first from Mgmt Portal to see if this is what you expect. 

the class documentation has a special warning:

As Security is a sensitive subject I think any other approach could cause serious damage or at least a risk.

<ZSOAP> is just a summary not more meaning than "there was an error"

for the details, I'd suggest to analyze variable %objlasterror

eg. set detail=$system.Status.GetErrorText(%objlasterror)

set fault.detail="<mymessage>"_detail_"</mymessage>"

An upgrade from Caché to Ensemble is not foreseen. 

Install ENSEMBLE in parallel to Caché and include your Caché Databases to Ensemble as you need.  

Attention: Ensemble is always running in Unicode!

You find it in 

Computer\HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Intersystems\Cache\Servers\<YourServer>

I found it by searching some  Webserver Port with regedit.exe 

Suggested approach:
Create a  namespace %ALL which is visible to all other namespaces and map the common class/table into it.
with global, package, routines whatever is related to it. 

See Mapping Data to All Namespaces  link