It has been answered several times, please, have a look here http://blog.archive.today/archive
Only one
There is no AJAX, just plain old <form> with POST.
You can make the same request using curl
http://blog.archive.is/post/45031162768/can-you-recommend-the-best-method-script-so-i-may-batch
It is not open source. May be I will release the current version as open source after switching to a newer one.
About API: you can submit a page by issuing a HTTP request with any suitable tool like curl or wget: http://blog.archive.is/post/45031162768/can-you-recommend-the-best-method-script-so-i-may-batch
It you need a more complex API, to perform searches, get answers in xml or json, etc, just let me know, I will implement it or find a way how to it.
something like
curl –data url=http://url-to-submit.com/ http://archive.is/submit/
Please note, that it may take up to 1 hour to process 7000 urls (after you submit them and before they will be visible on the site).
What kind of API do you need?
The site supports OExchange (http://www.oexchange.org/), so the bookmarking tools can use it.