There are a couple of different reasons that your camera isn't connected to the Wi-Fi, as described in our troubleshooting guide. You should make sure that you are within a reasonable distance of the router, as the camera will not connect if it can not find a strong signal. You should also make sure that the router is functioning correctly, and reset the router if necessary.
It is important to do these things when you are taking the pictures to ensure clear pictures, as described in our troubleshooting guide. Make sure the camera is being held steady. You can use a tripod to keep the camera steady. You can also select the OIS function and half press the shutter button to make sure the camera is focused.
There are a couple of ways to fix this answered in the troubleshooting guide. Before you take the picture, you can set the camera flash mode to red eye. If you have already taken the photo, you can use the red eye fix option when you are editing to remove the red eye.