What are Simulated B-mode and phantom images?
B-mode is the most elementary way to form an image from the Ultrasound modality. You basically shift the beam of an A-Mode, either mechanically or electronically. To simulate B-mode, you need a three dimensional model of tissue density and a sound propagation model. There are basically two methods to achieve it, you either do ray-tracing (if the wavelength is much smaller than the distance) or you solve the wave equation directly. In either of these cases you simulate ultrasound propagation through the tissue and re-construct the image that a real ultrasound machine would give you.

A "phantom", more generally, is an item that has been fully characterised and its measurements are known. It is used for calibration. So, for example, you know that Water should return a zero in the Haunsfield scale and Air should return -1000. If you scan a phantom and the image does not agree with its specifications, the machine needs to be re-calibrated / repaired. 

The simplest example of a phantom in "everyday life" is that gray-scale ribbon that you see in some screen calibration utilities that direct you to tune your monitor until you can see all the bands in the ribbon, or until some patterns appear / disappear.

A software phantom is exactly the same thing but it is used to "calibrate" or assess an algorithm. You are probably talking about the Shepp-Logan phantom which contains a number of fully characterised ellipses.

If you are working in tomographic image reconstruction then you can compare the image that your technique reconstructs against the "real" image and make inferences.

To create these images, all that you have to do is create an image with shapes of known characteristics (as you can see from the Wikipedia page on the Shepp-Logan phantom).

As far as the "...formula for signal-to-noise ration and contrast-to-noise ratio..." is concenred, it can be found on Wikipedia. It really depends on what you are trying to measure and how and yes, you will need a phantom for that. For more information please see this link.

Image quality assessment is a field on its own in medical imaging.

Hope this helps.