Hi ,
You can find the extension here http://marketplace.thingworx.com/Items/Twitter
a) Then in the mashup i suppose you can show all the twits or search for specific twits
b) update status
Note this extension does not facilitate multiple acc . configuration or login with twitter credentials ,
only one account can be managed through this
I found this another extesnion below
http://marketplace.thingworx.com/Items/Twitter-enhanced
this link does provide to download the extension but the plugin is broken it has only metaxml file
