While creating, controlling, and absorbing elements is nearly universal to all the different elemental powers are there other common applications of elemental powers that is shared by all or most elemental powers? For example sensing the user’s element such as a toa of green sensing roots underground, a toa of water sensing water in a nearby container, or a Makuta sensing a moving shadow that belongs to a person. Another example would be the creation of elemental creatures and weapons since even some of the intangible elements have been shown that they can be used this way is this use of elemental power applicable to all or most of the different elemental powers?
Yes, elemental users can indeed sense their elements. There are numerous examples throughout story of characters sensing or being distraught over loosing their bility to sense their own element:
The Toa of Water’s eyes flashed. “I cannot hear the water. I am deaf to the song of the waves Nokama, the ebb and flow of every river and stream on Mata Nui.I walk this land, but I am no longer a part of it.”
With unrelenting force of will, Onewa commanded the stone to reject that which did not belong. He could sense that the rock had interwoven with the substance of Matau and there would be no way to rip the Toa free.The rock would have to set him free. Painfully, inch by inch, he felt the stone retreat. Driven back by the power of the Toa Metru, it it released its hold at last on Matau.
“How did you –?”
“The stone is full of energy. Energy gives off heat,” said Lhikan. “Once I knew to look for it, it was easy. Heat is my business.”
The other thing you mentioned is possible too of course - things like stone fists, ice spears and even creatures of molten rock (like the one Avak and Hakann made) are perfectly normal for element users.