Cosmologists and Astronomers generally agree that the age of the universe is about 13.5 billion years. There are those who argue for a younger universe on the order of 8 billion years and there are some who believe the universe is nearly 20 billion years old. No one knows the exact answer but 13.5 billion years is acknowledged, by the scientific community, as the best educated guess we can make at this time.
The Bible does not give the age of the universe nor does it give an accurate age for the Earth. Those claims are pure conjecture, in fact, the book of Genesis allows for a very old age for the Earth. There are some who believe there were two creations...check it out for yourself.
As for dinosaurs and Noah, again, it seems most people listen to someone else's opinion instead of reading for themselves. The dinosaurs were long extinct before Noah ever came on the scene. Merlin's answer, in fact, is an excellent example of being told what to believe instead of reading and finding out for yourself. It is just a minor issue but it does demonstrate my point. According to the Bible Noah was commanded to bring in the animals but not only in two's. The fowl and birds were gathered in seven's as were all the "clean" animals. In fact only the "unclean" animals were gather in two's . So Noah was not commanded to gather "two" of everything....in many cases he was told to gather seven of each.
I'd like to issue everyone a challenge, for those who really want to know,....... "Unicorns" do you believe they existed or not...and if they did were they on the ark or ....did they miss the boat?