It’s worth noting that when you see a URL shortened to twt.tl it doesn’t mean that the contents of that link are bad. Twitter will simply re-route the user through to a stop page that prevents them from being affected
The main use of twitter is traffic and not backlinks. The shortened URLs are redirected from another server so it will not be counted as a backlink. So consider twitter as a method to improve your traffic. The shortened URLs doesn't affect your site in any way.
Its no different than any other link shortner as far as I know. Google can still see there's a redirect and what the final page is so there probably is the same SEO benefit as there was before.
Yeah you cannot use long URL for twitter because it allow only 140 characters.So you have to use shorten URL for this site.Shorten URL doesn't have any negative effect.Infact they are useful for SEO point of view.The click rate on long urls is very less in SERPS. It is very hard to write or to remember long URL for a common user.