Can Protein Be Changed Into Carbohydrates And Vice Versa?

Yes, this can happen. When plants photosynthesize, they manufacture sugars, which are carbohydrates. But the plants also need proteins. So, they manufacture their own amino acids by adding nitrogen to them and sometimes sulphur. Once these amino acids are made, they can be made into proteind by transcription of the protein code from the DNA in the cell.
Now, how can proteins be converted to carbohydrates. This is happening inside you all the time. Imagine you have eaten a big juicy steak for dinner. Now that is a lot more protein than your body needs. So, the body uses the protein from it (or makes its own protein form the amino acids of these proteins) and the rest of the protein goes to the liver. Here, deamination occurs. The ammonia part of the amino acids is first removed. This leaves behind an organic acid. The ammonia is converted to urea by the addition of carbon dioxide. This urea is then excreted in urine.
Now, we are interested in what happens to the organic acid. Well, this can be directly used for aerobic respiration or converted to lipids if there is already enough food to produce energy. These lipids can store energy as fat.
So, we still don't see where protein has been converted to carbohydrates. Imagine, the person is starving or fasting and has no intake of energy rich food. In this case, the body would break down the protein (from diet or from the body's own muscles) into organic acid (as usual) and this is converted into glucose which can then be used for obtaining energy.  
There you go, now you can see how carbohydrates change into proteins and vice versa.