Praise be to Allah (The Glorified and Exalted).
1) Yes, dinosaurs existed. There are many bones, and even one that was mummified has been found.
2) The age of the Earth in billions of years old and the statement that the dinosaurs were wiped out 60 million years ago, is just assumptions made by evolutionists.
3) From Carbon dating some dinosaur bones, they were found to be around 5,000 years old and others at around 16,000 years old. Blood has also been found in many bones. This, along with findings of a mummified dinosaur have led many to question whether dinosaurs really lived millions of years ago. There also accounts made by various peoples around the world in their oral traditions or preserved images on buildings that depict dinosaurs living on the Earth. This is a topic one has to research.
4) It is most likely the Earth is around 20,000 years old (estimated from various studies) and the humans in the past lived with dinosaurs for a time, considering the entire nature of the Earth was gigantic. Most humans made their homes within mountains or large pyramid structures made of stones, or caves, etc. Therefore, they could have survived together. There is a hadith that mentions that Adam (peace be upon him) was gigantic in stature along with the rest of the nature of the Earth, but later generations were permitted to shrink in stature until the time of the Prophet (peace and blessings of Allah be upon him). As the humans in later generations shrunk, so did the animals and plant life in later generations. It is already accepted in modern times among all persons, that insects, animals, and plant life in the past were gigantic. The part about giant humans is debated by biologists. There are many oral traditions from peoples from around the entire Earth, speaking about giant humans that once lived on the Earth. There are also some assumed graves. This is also another topic one must research in order to fully understand and accept.
5) Much of the fossil fuels used to power the modern world come from the remains of dinosaurs, and other animals, and plant life that once existed in the past. Therefore, it makes since that Allah (The Glorified) would have allowed these animals to inhabit the Earth and for the Earth to exist for a time before humans inhabited it. Because some time is needed for these decomposed animals and plant life to be turned into usable fossil fuels.
6) The Qur'an is a Book of Revelation teaching mankind to worship the correct God, and other various lessons, and warning them about the Day of Judgment and Heaven and Hell. It has nothing to do with teaching history, or biology, etc.
7)
First the Djinns (the tribe of Iblis) lived on earth and we don't know what animals lived on earth before mankind started to live on it with the Djinns.
This is an assumption made from people's traditions and is not mentioned in the Qur'an or any hadith. The first jinn was Iblis and he came to the Earth during the time of Adam and Hawwa (peace be upon them). The Iblis is the father of the jinn race, his female mate is note mentioned, but it is likely he had one as well, considering jinns procreate like humans.
8) If your parents, with their level of knowledge and education do not accept the existence of dinosaurs, do not push it, although it is incorrect. It is not appropriate, and they will not be questioned about it on the Day of Judgment, just as many humans in the past believed that the Earth was flat, that will not effect their salvation.
And Allah (The Glorified and Exalted) Knows Best.