Then a wide focal length is the ideal, which you already got - 18mm on a T2i (1.6x crop factor) is ~28mm on a full frame. Wider than that and you'll start getting some serious perspective distortion you'd need to correct.
sports mode photography
Then a fast telephoto and good AF is essential. You already have a telephoto, depending on what sports you're shooting and what quality you want to achieve that's all you need. Since you said you're a beginner, unless you have money to spend I don't think it's necessary to get a fast telephoto with a good on-lens AF motor (which would be very expensive).
and some portrait shots of friends and family
Again, you already have a nice focal length range for that. If you want to get better quality on those, get a better glass. 50mm fast prime lenses usually are the best cost-benefit alternative for that.
Taking pictures of buildings at night is really difficult, specially if there is some street light around etc
Instead of a better lens consider getting
- A better angle
- A tripod
- Photoshop if you really really don't want the street lights on the picture
A wider lens might help you there too, but then again there's distortion. A tilt shift is probably the best lens for taking pictures of buildings (specially tall ones), but it's absurdly expensive and require some skills to use. A faster lens might help with the low-light issue, but a tripod is cheaper and better for that (I'm not saying it substitutes a fast lens, I'm just saying it might be best for the OP).
I love taking pictures where background is blurred. Unfortunately, with 18-55 lens, I have very limited angles to make it possible
The most important thing here is the aperture not the focal length. The wider the aperture, the blurrier the background (the shallower the depth of field). A larger format would also provide a shallower depth of field.
To sum things up: I don't think you need a new lens, but if you want to get one, get a fast prime.
- The AF will probably be better for sports
- The quality will probably be better than the kit one's
- It'll make low-light photography easy
- You already have two zoom lenses