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How to design own checkout.js similar to paypal or stripe

Paypal and Stripe provides their own checkout.js. Client app/website integrates the checkout.js in their payment page to enable Paypal/Stripe payment button in their interface.
I want to know, if I had to design a similar checkout.js for a payment gateway, what are the things/components to look at? Is there any guidelines/ best practices available on the internet on this? And, is checkout.js really a efficient solution to enable client apps integrate with your payment solution? If not, is their any alternate / better way?

As is the case any time you decide to blaze your own trail when handling sensitive information like credit card details and passwords- proceed with extreme caution. One simple slip-up or oversight could potentially leak your customer's card details to the "bad guys". In short- don't do it.
If you're still trying to create your own checkout solution after considering the above advice, Stripe's documentation on how to use and customize their Checkout form is a great place to start.
Anecdotally, I can vouch for the effectiveness and ease-of-use of Stripe's checkout plugin.

Web UI for a REST API

I wrote a REST API in Node.js (with Express)that implements a queue with some dequeue/enqueue functionality, and the next step is creating a web view for that API.
I am really new to javascript and Node.js , can i have some pointers on how to implement it? is there a framework I can use to integrate the api.js i built with a front-end?

When you wrote a REST api using nodejs and the expressjs framework, you are perfectly prepared to use the complete MEAN stack, which implements angularJS for frontend services.
Angular offers a complete REST implementation (called ngResource). Install via npm.
With the angular resource service you get your frontend interface (to interact with your backend) out of the box (except a few adaptations you'll have to make, e.g. to make it work with Mongoose, which is used to make the access to your MongoDB more comfortable).
You'll find a few superb tutorials, as this one and others on scotch.io are some of them. Google for 'api rest angular resource mean ...' in different selections ;-)
Other links that helped me a lot:
Tutorial from Angular itself
Thinkster.io - complete MEAN stack overview with examples
a helpful tutorial with good examples from Frederik Dietz
Buecheler comes out with this great tutorial, but its more about the backend side - as you might check your code againt the basic standards of a REST backend implementation.
Those are some of the links I noted and that could find ad hoc.
EDIT:
As your headline suggests you are searching for an UI, I suppose IBM Strongloop might be a good hint for you. IBM is strongly interconnected with the development of ExpressJS and offers this API and UI for probably all data concerning questions of your Webapp.

Nativescript push notifications with 3rd party Push services

I'm getting ready to build a Cross-Platform app using NativeScript and was wondering if the Push notification package they offer supports integration with 3rd party push services. I would think so, but I notice some of the sites for the push services actually list the Dev Platforms they support. Carnival for example has a special package for React-Native. Any one have any experience with this?

I saw that you have already found your answer in Nativescript repository but in order to share the knowledge with the community I am going to post the link to the discussion here
As Brad Martin said - Yes - you can use 3rd parties services.
Anyone interested can see his article on that matter here

Is OpenSocial a viable API choice?

For a project we're looking at a mechanism to import gadgets (friends lists, todo lists, etc) from other sites, something that OpenSocial is supposed to be great at. However, I'm concerned about whether or not OpenSocial is dead. Many of the API pages for OpenSocial 0.9 haven't been updated since April 2009. The few recent updates I have seen are just spambots posting links to cheap german pharmaceuticals (for example, see this history page).
Is OpenSocial alive? Or has it, like so many other grandiose ideas, been abandoned to the wastes of the Internet?

Indeed OpenSocial is definetely not dead. Although the OpenSocial spec has started as an alternative or competitor to Facebook platform to be used in consumer oriented social networks, the spec and accompanying open source implementation Shindig evolved into a more general API framework and a common data model which adresses use cases from consumer to enterprise portals and groupware solutions. While Facebook platform dominates consumer web and may be a natural choice for external identity support or content distribution, OpenSocial is being used inside ever increasing products and integrated to various cloud applications.
Current work in progress spec version is 2.0 and an active community discusses several new features that contribute to building a more open social web. You may see what is being developed here (http://wiki.opensocial.org/index.php?title=Spec_Changes) or join the community to monitor progres or contribute to the spec here (http://groups.google.com/group/opensocial-and-gadgets-spec).
Regarding your use case, OpenSocial may help you by supplying a client side JS based mash up container. With recent Open Ajax support and a JS container, OpenSocial (and Shindig) may easily serve as a dashboard or client side portal. We could sucessfully developed on top of Shindig a self service portal that can integrate gadgets from third parties or of our own developed ones. The Rest API also helps in developing server side applications.
So I strongly recommend to look deeper in OpenSocial for your specific needs.

App Engine and Facebook: which libraries to use?

I will be developing a web application with Google App Engine that will use Facebook Connect as the only means of registering / logging in. The web app will be written in Python. I need to know their name, profile pic, how many friends the user has, as well as their age and also possibly location, relationship status, work info, etc. (although those are mostly optional besides name, pic, age and friend count).
There seem to be a number of libraries that can do the task. There is the official Facebook Javascript SDK, minifb, and pyfacebook to name a few.
How do you think I should go about this task? Which libraries should I use, and what are the pros / cons?
Also to be considered is how well documented the code is and how widely it is used. If you can provide links to relevant example code / documentation, that would be greatly appreciated.

Facebook python-sdk has an example application to use Facebook connect with Google App Engine. I guess, you are looking for the same.

This should be a comment for the answer which suggests using the Facebook python-sdk.
Note that at github it says
This SDK is deprecated. It does not support the new cookie format that
we rolled out as part of the OAuth Migration. In short, it doesn't
work.
I've had success with the facebook-sdk project, which I believe is a fork of Facebook's original (and now dead) python-sdk project noted above. However you may also wish to check out EngineAuth.

Why don't you check out this similar question asked by another StackOverflow user:
Simple Facebook Connect in Google App Engine (Python)
There are some links provided here that sound exactly like what you're looking for.

For all specified detail you need to go with respective permission from users and then you can extract all specific information you needed.
You can go by either Graph Api or Javascript Api:
But with javascript you need to use many ajax request through your application where graph api only need access_token once for particular instance and also independent of client action.
Graph API also helps you in preventing use of other framework like pyfacebook, minifb, etc.
Apart from pros and cons you can also look some example code for both javascript and graph api
Hope this information will be useful to you.