You can use SuiteTalk APIs to track orders in any Server side language of your choice. NetSuite help has details on consuming the SOAP APIs in Java and PHP, for other languages you may to do some extra effort, but, it is possible.
In SuiteTalk there are APIs for Sales Order and Item Fulfillment so, that you can track order details as well as its fulfillment and shipping details.
You can search, update, create and delete orders/fulfilments from SOAP/Suitetalk APIs.
the documentations are available here as Records Guide and here as platform Guide (Might require logging into NetSuite)
Alternatively, you can write RESTlets in your NetSuite account using NetSuite's Suitescripts and bundle them (if you want to use across other NetSuite Accounts), and then use HTTPS requests from your server side language to do the CRUD operations on order/fulfulilment records.
How do I track the order on frontend as a customer using Nestuite
Order Tracking API ?
From front end, I suggest to write a middleware or a web server that speaks to NetSuite APIs, as you would not want to expose the NetSUite credentials/tokens required by APIs
Is there any already available API's that supports the above feature ?
Yes, please see the linked PDFs on syntax/API help on searching/listing orders/fulfilments or else write your own RESTlet code using SuiteScript and HTTPs it.
How and where do I test if any API for order tracking is available ?
You, need to have access to a NetSuite account for that. You can request NetSuite if you are a SDN partner for a test account. If your company is not a SDN partner you can request a community supported test account using your company's email id only.
Working on localhost, what change should be done in NSConfig.php
parameters to test sample API's provided ?
You cant test on localhost, you got to have a NetSuite Account
$nsendpoint = "2015_1"; //not required to change
$nshost = "https://webservices.netsuite.com"; //once you obtain the NetSuite account will vary based on you data center
$nsemail = "jDoe@netsuite.com"; // your login email
$nspassword = "mySecretPwd"; // your password
$nsrole = "3"; //your role Id (if you are an admin you can leave it)
$nsaccount = "MYACCT1"; // your netsuite account Id