F5 iControl REST - API calls required to get Load Balancer, Virtual Server URL, IP, Port, Pool Name/Status/Members

I did something similar using Powershell 4.0. You are also going to need the BIG IP 11.5.3 (I guess at least), I'm using 11.6.1. Maybe my code can shed some light for you... it's a very simple one:

    function Get-F5Token(
[Parameter(Mandatory=$True)] 
[string]$currentf5
)
{ 
    $username="admin" 
    $password="admin"
    $url="https://"+$currentf5+"/mgmt/shared/authn/login"
    $payload='{"username":"'+$username+'","password":"'+$password+'","loginProviderName":"tmos"}'
    Convert Username/Password to Base64 and create Header
    $bytesauth  = [System.Text.Encoding]::UTF8.GetBytes($username+":"+$password)
    $authvalue = "Basic "+[System.Convert]::ToBase64String($bytesauth)
    $headers = @{ Authorization = $authvalue }

    return ((Invoke-WebRequest  -headers $headers -contenttype "application/json" -Method POST -uri $url -body $payload).content |Convertfrom-Json).token
}

 Allow self-signed certificates
[System.Net.ServicePointManager]::ServerCertificateValidationCallback = {$true}
$global:Authentication = (Get-F5Token 10.10.66.92)
$global:tokenheader = @{ "X-F5-Auth-Token" = $Authentication.token }
  Create timer
$backgroundTimer = New-Object System.Timers.Timer
 Set interval (ms)
$backgroundTimer.Interval = 5000

 Make sure timer stops raising events after each interval
$backgroundTimer.AutoReset = $true

if((Get-EventSubscriber | where { $_.SourceIdentifier -eq "renewToken" }) -eq $null){
     Have powershell "listen" for the event in the background
    Register-ObjectEvent $backgroundTimer -EventName 'Elapsed' -SourceIdentifier 'renewToken' -Action { 
    $global:Authentication = (Get-F5Token 10.10.66.92)
    $global:tokenheader = @{ "X-F5-Auth-Token" = $global:Authentication.token }
       Restart timer
      $backgroundTimer.Start()
    }

} 

 Enable the timer, with that we will get a new token every 5 seconds.
$backgroundTimer.Enabled = $true

Get information regarding this F5:
$ltm  = new-object Psobject
$ltm | Add-Member irule $null
$ltm | Add-Member pool $null
$ltm | Add-Member vs $null
$ltm | add-member policies $null 

$ltm.policies = @(New-Object psobject -Property @{
            vsname = $null;
            policy = $null; 
            })

Now all the informations regarding VirtualServers, Irules, Pools are going to be in the object called $ltm