1. Distance from Object = Focal Length x (Actual Height of Object / Height of Object on Sensor)
hence d = 300 mm x (304.8 mm / 15.6 mm) {bird 12" high = 304.8mm, APS-C Sensor height = 15.6mm}
d = 5861.53mm = 19.2 feet
More at:
http://www.rajib.com/going-to-forest-safari-what-zoom-lens-should-i-take/824/2. Sharp Print: technically, there are 2 points of consideration
a. Number of pixels required to print a 24" photo: Assuming, that the photo follows 3:2 ratio, hence the photo is 16" x 24". Assuming printing is done at 300 dpi (90K dots per Sq. In.). Hence Total number of dots = 16 x 24 x 90000 = 34,560,000. If each dot is represented as pixel, the image requires a 34 MP camera. In real-world however, interpolation can save the day and you should be able to generate a pin-sharp print from a 16-18 MP camera.
b. Distance, Focal Length, Optic Quality: These vary very widely. For ex: If you only have access to a 18-55mm lens, you will need to get quite close to the subject to obtain a Full-Sensor image. Even if you use a 70-300mm lens, the optics are likely to perform poorly at the extreme ends of the lens capability. i.e. your lens may give better images at 200mm focal length than at 300mm. Optic quality is subject to the glass used and also the general shooting conditions (haze, dust, wind etc.).
3. Question #3 is similar to #1 & #2 and I hope has been answered to your satisfaction.
HTH