Hi Rio,
I think the summary your provided is over simplified. For an example you say that in Shaivism they worship Shiva as the supreme Deity and use ashes in ritual. Actually many hindus use ashes in ritual. Shaivism itself is filled with different paths. There is nondual shaivism and there is also dualistic shaivism.
My favorite and chosen path right now is Kashmir Shaivism. In this path Shiva is worshiped, but so is his Shakti (the great Goddess). The whole purpose is more than worshiping a Deity form outside of oneself, but instead is to realize the unity that already exists between Shiva (Consciousness) and the ordinary individual.
To have a better understanding of the different sects you mentioned above please visit this link:
http://www.himalayanacademy.com/read...cing-with-siva
Go to the section on "What are Hinduism Principle Sects"
I think you will be happy with the summary of each sect.
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http://youtu.be/xVi2ueJrYPk Kashmir Shaivism 1
http://youtu.be/jhDOKZW2Vsg Kashmir Shaivism 2
http://youtu.be/sKfb5iY1Or4 Kashmir Shaivism 3
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