According to documentation,  the tformat paramer 5 is ignored:

"Specify time in the form "hh:mm:ss+/-hh:mm" (24-hour clock). The time is specified as local time. The following optional suffix may be supplied, but is ignored: a plus (+) or minus (–) suffix followed by the offset of local time from Coordinated Universal Time (UTC). A minus sign (-hh:mm) indicates that the local time is earlier (westward) of the Greenwich meridian by the returned offset number of hours and minutes. A plus sign (+hh:mm) indicates that the local time is later (eastward) of the Greenwich meridian by the returned offset number of hours and minutes."

The same goes for the parameter values 6, 7 and 8

write $zdth("2021-11-04T11:10:00+0100",3,5)  --> 66052,40200
write $zdth("2021-11-04T11:10:00+0200",3,5)  --> 66052,40200
write $zdth("2021-11-04T11:10:00-0100",3,5)  --> 66052,40200

OK, I start with the second question. I'm not aware of a function to see if a specific global is in a buffer or not but there is a routine which shows which globals are using the most buffers:

znspace "%SYS"
do ^GLOBUFF

For the first question: if a global is used continuously, then it will always be in buffer. That's the simple answer. The reality depends on many other factors: the size of the global, the size of the buffer pool, how many other globals are in use, how often is a global used, etc.

To keep a few specific global(s) always in a buffer, there is a simple trick (assuming, your Cache/IRIS installation uses the default setup and you have an unused block size):

1) Goto SystemAdministration-->Configuration-->AdditionalSettings-->Startup: and edit the DBSizesAllowed setting, by checking one of the 16K or the 32K checkboxes

2) Create a new database with the newly enabled block size. This database will hold those few (always needed) globals.

3) Goto SystemAdministration-->Configuration-->SystemConfiguration-->MemoryAndStartup: and allocate (plenty of) memory for the newly created buffersize. Please consider,  after this chanhe, you have to RESTART your system!

4) Copy the global(s) in question into the newly created database:

  merge ^|"^^c:\path_to_new_database\"|GlobalName = ^|"^^c:\path_to_old_database\"|GlobalName

5) Create a Global mapping for the globals in question to the new location.

6) Start working... If everything is OK (which should be) and you are happy, delete the old global data to free up database space:   

kill merge ^|"^^c:\path_to_old_database\"|GlobalName

7) In a standard installation, you have allocated  one buffer pool (with the standard 8KB buffer size). So all your processes faiting to get the needed globals into that buffer pool.

With the above configuration you have two buffer pools, one for the standard 8KB database blocks and one for the new 16KB (or wahtever size you have choosen) database blocks. So you can keep important globals in a separate buffer pool. If you can manage (this will be application dependent) to give this buffer pool the same size as the database itself, the you will have all data (of this database) in the memory all day long.

I fear  you have to be some kind of a magician, to solve this problem...
You need  two things (a) a time-zone-offset, which is not the problem (it's more or less static) and (b) DST-offset, which is a problem, because there are databases for the past but not for future. Maybe you can put the DST-offset into a global for each of the geographic region you need. And yes, you have to maintain it...

Some starting points:  https://en.wikipedia.org/wiki/Tz_database  and http://web.cs.ucla.edu/~eggert/tz/tz-link.htm. In case you you work with python, take a look at https://pypi.org/project/pytz/

The README file from tz_database says the problem in a nutshell:
"The Time Zone Database (called tz, tzdb or zoneinfo) contains code and data that represent the history of local time for many representative locations around the globe.  It is updated periodically to reflect changes made by political bodies to time zone boundaries, UTC offsets, and daylight-saving rules."

He (@David Hockenbroch) is playing with inderection, using $classmethod() instead of ##class(classname).methodname(...)  does not solve the scoping problem:

ClassMethod testvalidator(class As %String, value As %String) As %Status
{  
  set validator = "sc = $classmethod(class, ""IsValid"", value)"
   write validator,!
   set @validator
   write sc,!
   quit sc
}

The above method gives you the same <UNDEF> error because of non global scoping! By using indirection both variables (validator and sc) must have global scope.

As @Sergei.Shutov pointed out, you can switch off the procdere block by a keyword for the whole class. Additionaly, you can switch on or off the procedure block keyword for a particular  method too. In your case:

class Some.Class  Extends %RegisteredObject
{
/// a procedure block method
ClassMethod ProcBlock()
{
}

/// a nonprocedurblock method
ClassMethod NoProcBlock() [ ProcedureBlock = 0 ]
{
// Caution: All variables have a global scope, hence, they will overwrite variables with the same name, which were created previously. To avoid this, use the NEW command, to protect them (if desired).
}

}

You have a problem with the scoping!

Indirection has a global scoping, you have to put things with indirection in a global scope:

ClassMethod testvalidator(class As %String, value As %String) As %Status [ PublicList = (validator, sc) ]
{
   new validator, sc
   set validator = "sc = ##class("_class_").IsValid("""_value_""")"
   write validator,!
   set @validator
   write sc,!
   quit sc
}
set result = ##class(...).testvalidator("%Library.Numeric","BLABLA")
do $system.OBJ.DisplayError(result) --> ERROR #7207: Datatype value 'BLABLA' is not a valid number

According to the task, "...You will receive an integer number and you will return a new number..."

set s=9999999999999999999
write s --> 10000000000000000000
write AddWater(s) --> 1  // which is the expected result

The above method works also for cases, where s contains a string of digits

set a="9999999999999999999"
write a  --> 9999999999999999999
set res=AddWater(s)
write res ---> 999...<165 more nines>...999
write $length(s) --> 19
write $length(res) --> 171  // 19 * 9 = 171

So why do you show those devils?

There is one thing you should check, than this could trigger effects observed by you.
Objects are tracked by reference counts, as long as an objects reference count is greater then one, locks won't be released and the object isn't deleted.

set obj = ##class(Some.Class).%OpenId(id, 4) // the obj's ref count is one
... // more commands
    // now, the application does something like this
set tmp = obj    // obj's ref count is now two!
... // more commands

set obj = "" // the application intents to close the object
             // but the object still exists due to the fact that the ref count is one
             // (the object is still referenced by <tmp>)

There are methods to detect such a situation:
- $system.OBJ.ShowObjects(), lists all objects with reference counts
- $system.OBJ.ShowReferences(obj), list all variables which contains a reference to <obj>

A quick and dirty approach:

set filename = "...some file name"
open filename:"nw":0
if $t { use filename
        do $system.ShowObjects()
        do $system.ShowReferences(obj) 
        close filename
      }
set obj = "" 

Give it a try, maybe your object has multiple references which cause the problem

The %SYS.Namespace class contains the methods, you are looking for.

write ##class(%SYS.Namespace).GetGlobalDest( [namspace], "global") --> DB where the global lies
write ##class(%SYS.Namespace).GetRoutineDest( [namspace], "routine") --> DB where the routine lies
write ##class(%SYS.Namespace).GetPackageDest( [namspace], "package") --> DB where the package lies

If you create a class, you can it declare as a hidden class, see

https://docs.intersystems.com/iris20211/csp/docbook/DocBook.UI.Page.cls?...

Class My.Class Extends What.Ever [ Hidden ]
{
}

will be a hidden class.  

For your own classes you can adjust this class keyword as you like but for the system classes - there is no chance, they lie somwhere on ISC servers (and, but this is my very own opinion, not very wise. First, I would like to read the documentation for the version I have installed (and not always the latest version) and second, I would like to read the doc everywhere! For example, I have a 10 hour flight, and want to work. And in case, a server only has a  local LAN access, then you have no docu!).

set old = ##class(%Stream.TmpCharacter).%New()
do old.Write("This is my text")

So, now you have an old stream, "This is my text" but want to have a new stream as "This is my NEW text".

set new = ##class(%Stream.TmpCharacter).%New()
do old.Rewind()
set pos = 10 // This is my
do new.Write(old.Read(pos)), new.Write(" NEW"), new.Write(old.Read(old.Size-pos))

And now, check the resulty

do new.Rewind()
write new.Read(new.Size) --> This is my NEW text