Asalam wailkium, welcome to TTI. The answer to your questions are huge as each of them are broad topics, i will summarise each one as follows.
1) What is the purpose of animals described in Islam?
Allah; almighty god is the creator, he loves to create all forms of unique creatures, their (animas/plants) diversity and greatness which we learn from observations in daily life and their complexity which we learn from science shows us how great the creator of life is, the beauty, power and might of our lord, god almighty. So they are proof's for the existence of the creator, signs of the creator's handiwork, as be say such beauty order and complexity cannot occur by mere chance.
The creatures also serve/worship god by maintaining the Earth for human beings, Allah doesn't need them to do so, but this is his system, this is how he chooses to govern our reality by creating servants to carry out various tasks. Apart from maintaining the ecosystem and being a reflection of god's greatness the other reason is for them is to provide us food and raw materials for us for our own benefit, this is from the mercy of god so we can live and survive.
2) What chracteristics do they (animals) have?
They each have a specific task to do which god has created them for, thus they worship god because they are carrying out their individual tasks which they have been specifically designed for. They follow their innate animalistic raw desires all the time where as humans have a balance between desires and the logic.
3) What are the differences between animals and human beings?
That ability to using logic, the human mind, to ponder over things with reason and understanding is the crucial difference between us and animals. Our task is slightly different, ours is to maintain the Earth like a steward would, following the rule of God so that peace, goodness and justice will prevail over evil, tyranny and false ideologies. This has been shown to us through the example of the prophets and the revalations. So human beings have a greater responsibilty compared to animals thus we are created differently more advanced, and will be judged regarding that responsibility and our justice on how we managed our affairs on this Earth. Animals don't have that grand responsibility and therefore there is no heaven/hell, serious accounting for them in the afterlife.
These are some brief major points i have mentioned. I hope it answers your questions, feel free to ask more.
