Well your questions are all over the place, and it's not really clear what your issue actually is.
You may read the Twitter plugin manual article and see that to display it as a big image you need to modify the "Size" property of the object.
Otherwise, create your own image and use the Browser plugin "Go to URL" action.
The URL to use is something of :
[quote:2c7n8s2i]https://twitter.com/intent/tweet?original_referer=XXX&text=My%20score&tw_p=tweetbutton&url=YYY
Playing with that URL will allow you to make the message how you want and make it look/refer to the twitter account of your choice.
This has more to do with twitter's API.
Finally, Facebook and Twitter are two different social networks. Although it is easier to provide a tweet through an URL than a complete Facebook post.
Twitter might also be a bit less intrusive than FB. But I guess that depends on how you use it.