How to make applescript type items into url bar

Probably not the only way to do it... And these are not my favourite type of scripts.

But here is an example of each of the syntax you describe.

Look up:

• message viewer
• selected mailboxes
• selected messages

In the Applescript library for Mail.

tell application "Mail"
    set theMailID to 543521
    set theM to mailbox "INBOX" of account "iCloud"

    set selected mailboxes of message viewer 1 to theM
    set sort column of message viewer 1 to from column
    delay 0.5 -- important delay or message selection may not happen
    set selected messages of message viewer 1 to (first message of (theM) whose id = theMailID)

end tell

You won't be able to do it in AppleScript : Safari only does something on open windows.

You should definitely look at Command line scripts like curl.

The AppleScript to call a shell command takes the form:

set variableName to do shell script "command"

So using your AlertURLString you'd want something like:

set curlOutput to do shell script "curl '" & AlertURLString & "'"

See the curl man page for more details on how to use curl to do things like POST and PUT calls or attach payloads to the calls and what not. It is incredibly powerful.