Only for non moving subjects
I agree, looking at those 3 shots on the PC they all look like camera shake is more of a deal than subject movement to me at least.
3795.jpg - the sparkler/torch scene is a 2 second exposure at 30mm, F4.5 and 3200ISO - not much is going to preserve the lighting of the shot without showing some blur on the people. If it is a bunch of sparklers you're going to get some movement from the lighting. A faster lens and higher ISO might have worked but still a big ask.
3813.jpg - the silhouette of people is 1/8th of a second at 50mm, F5.6 and ISO3200. A faster lens would definitely have got that down to a speed you could hand hold, but that person's arm would probably blur out anyway.
3816.jpg - is 1/15th at 35mm, F5.0 and ISO3200. A faster lens would definitely help, you could probably have used flash without ruining the scene.
Based on the focal lengths then I guess a 35mm prime would be worth a look.