The orange color in carrots is caused by beta-carotene, a precursor to Vitamin A. [This is found in the food itself. Our own genes do not take up the function from the carrot gene]. We eat carrots not only because they taste good but because they are a good source of thisnutritious compound. Over consumption could in fact lead to your skin taking on an orange tinge. Humans should generally never consume too much of any one thing. Moderation is always best.
Regarding your second question. This is not true for several reasons. DNA is present in all plant and animal cells therefore we consume it on a regular basis. It is digested along with the protein, carbohydrates and fats that we also consume in food. It is pretty clear that DNA consumption does not lead to humans or any organism taking on the attributes they consume. This is true regardless of the source of the DNA (transgenic or nontransgenic, plant or animal). Likewise, the microflora in the gut does not assimilate DNA from the food its host consumes. So, transfer of genes does not regularly occur.