Start shooting and learning in P mode and understand then what the camera is doing. The kit lens is fine, I used it for a long time before I went out and bought new lenses. AND I got some pretty awsome shots with it.
Try using the flash the camera came with. When shooting indoors like that, use a flash. Try keeping the camera as still as possible.
Remember, when using AV mode inside, with flash, its going to be fill flash, which could cause problems shooting in low light in doors, so be sure to use P or Manual mode, or AV once you get more experience.
When using flash, try ISO 100, 200, or 400.
Shots look like they also suffer from bad auto focus. Try focusing with the flash up too, it CAN help. I know spending $ after the fact isnt always the best solution, but you might want try and look into getting a used flash unit like a 420ex. Going rate is about $150 shipped used.
After getting my flash unit, it improved my low light indoor photography dramatically. Both in autofocus in low light since the flash has an AF assist beam, and power output.
Good luck.