Lord Hanuman is an avatar of Lord Shiva:
It is believed that Hanuman is the eleventh reincarnation of the Lord. Also, Hanuman is often recalled as Rudravatar, or the reincarnation of Rudra and Shiva is also known as the Rudra. The vanaras or the ancestor of human had helped Lord Rama(Reincarnation of Lord Vishnu) in the mythology of Ramayana. Without their support, Ravana could not have been destroyed. Hanuman is, by people, often worshiped for his devotion to Lord Rama and his part in the "good over evil." It is also depicted as the utter and infinite devotion of Lord Shiva to Lord Vishnu, as he reincarnated as a monkey and served him with all he had.
The story of Amarnath Cave:
Amarnath Cave is of utmost importance for followers of Lord Shiva. The legendary importance of Amaranth'scave is related to the secret of immortality told to Lord Shiva's wife Parvathi. When Lord Shiva insisted by his wife to revel the secre of immortality, he decided to proceed towards the cave. On his way to the cave he did a few things, which were great according to his devotees. Because of these few things, the entire way to the cave becameblissful. Actually, in order to reveal the secret of amar katha, Lord shiva left his son, vehicle,etc in various isolated places,which is why all these places seem like thirthashal. There are two ways for Amarnath journey - Pahalgam and Sonmarg Baltal. According to mythology. Lord shiva too the Pahalgam route to reach the cave.
Why Lord Shiva Coveres His Body With Ash :
Lord Shiva's body is always covered with ash and Shiv devotees wear ash tilak on forehead and hands. There is an intresting story in the Shiva Purana which narrates how Lord Shiva came to be associated with Ash.There once lived a sage whose lineage was traced to the famous Saint Bhirgu. This sage performed intense austerities and became very powerful. He used to consume only fruits and later only green leaves and thus got the name - Parnada.
Sage Parnada continued his intense tapas and controlled all the animals and plants in the forest he lives. Once while cutting some grass to repair his hermitage, the sage cut his mindle finger. But to his surprise instead of blood he saw sap of tree oozing through the cut.
Now Parnada thought that he had become so pious that instead of blood, sap is oozing through his body. Pride filled his mind and he started shouting in joy that he is the most pious man in the world now.
lord shiva who witnessed this event took the guise of an old man and reached the spot. When the old man asked for the reason for his uncontrollable delight, Parnada said that he has become the most pious man in the world as his blood as become quite similar to the sap of fruits and trees.
Then the old man asked what is there to be elated in this. It is just a sap. But when trees and plants are burned they turn into ash. Only ash remains that is surely the higher stage.
To demonstrate in the old man sliced his finger and suddenly ash came out of it. Sage Parnada soon realised that it was shiva standing before him and prayed to him for forgiveness for his ignorance.
It is said that ever since then Shiva wears ash to remind his devotees about the ultimate reality and foolishness of getting enamored in physical beauty.