I want to use Twitter API so my program can post some tweets. To use it I have to register application in dev-center and get some parameters like "Consumer key", "Consumer secret" etc. Then I can use either REST API, or some libraries like twitter4j - OK, that's simple.
But the question is: who will be the "author" of such tweets? Or, in other words, where can I find them after posting? Will they be posted by application or by some user? I can't really figure out how particular user binds to registered API-application... Or how can I specify ("log-in") user to post tweet on behalf of?
The "author" is always going to be the authenticating user. From the Twitter API documentation for statuses/update:
Updates the authenticating user's current status, also known as tweeting.
To answer your other question about authenticating with another user's username/password, it is possible but you need to get permission from Twitter. You also still need to use OAuth. Check out the Twitter API OAuth documentation.