There are several different factors, here.
The pop-up flash is different from the YN-660, in that it can talk back to your camera. If you look on the foot of the YN-660, you'll see that it only has a single pin. That pin is for the "fire" signal. That's all the camera hotshoe can tell it to do. The other three contacts on your hotshoe are for things like TTL, HSS, remote power control, etc.
So, that's why your flash is firing. But if you are in Av mode, and the camera is set up to expect TTL flash (as with your pop-up), there's a problem. TTL is when the camera tells the flash to send out a small "preburst" of light to meter, and then the camera adjusts the power on the flash based on the metering results before taking the picture. Your YN-660 can't ack back or have its power set by anything but a YN-560-TX over radio. So when the flash fires, it will most likely only fire at full power.
The slow shutter speed is also because you are in Av mode. TTL metering isn't getting that pre-flash, so it's metering a very low light level, and the auto-exposure in the camera is setting a very slow shutter speed to accommodate this low light level. You could try using Tv and setting a hand-holding shutter speed that works, and it could help. Or using P mode (which is more liable to keep you from using slower shutter speeds). But the problem remains that you have to dial the flash power in on the flash itself. And M mode on the camera still remains the best way for you to control flash/ambient balance.