Yes, the Sitecore Item Web API can be used to create items via HTTP POST requests.
You do this by POSTing to a URL such as this, to specify the parent item and template to use:
And field contents are provided as a
x-www-form-urlencoded body, e.g.:
The full documentation for the Item Web API has more details, including how to manage the security of this API. Though it states up to Sitecore 7.1, this documentation is also applicable to Sitecore 7.2.
With respect to item buckets, you can use the standard API for this. As long as the new item template is set to be Bucketable in the
Standard Values, and the parent item you are creating the new item under is a bucket, this will be created as a bucket item without needing any special treatment.