Hello everyone! I want to ask some questions...
What are the main concern/ objectives of the ionian school of thought?
The Ionians which include the atomists, the Pythagoreans and others, essentially were concerned more with the physics and cosmogony than with epistemology, metaphysics, ethics, logic etc.. Basically, they were much closer to today's modern physicists than were their successors, Plato and Aristotle. Socrates used to say that "ruminations on such matters as the heavens and astronomy is futile and foolish." Such was the trend he would set for 2,000 years.
Thales said that the essence of all things is water. Why?
Early philosophers seemed to work from a basic set of axioms, one being that the universe was in constant flux (though some did disagree with this to be fair) and one that everything is made from the same substance (monism as the previous poster said). Thales' conclusions were simply a result of his ratiocination on this matter with the aforementioned axioms taken into account. Thales is also credited with making the first correct mathematical predictions of a solar eclipse, though some think he may have been unfairly given credit for this as the cycle was already long known before his time according to some.
Anaximander said that the lump of material that is infinite and eternal called apeiron ("The Unlimited") is the essence of all things. Why?
Anaximander, along with Heraclitus and Democritus, is my favorite of the Pre-Socratics, and is also someone that was far ahead of his time with his speculations. Were you aware that Anaximander, instead of telling the usual tale of creation associated with the Gods of Olympus as Plato and Aristotle did, believed that human beings had "evolved" from fish (which is correct according to modern Biology)? Say hello to Darwin for me.
As for your question, he believed the apeiron to be the basis of all things because of the axioms I mentioned above. Most of the pre-Socratics believed that the universe was comprised of the same "Stuff" but just in different forms (which really isn't that far off the mark).
Heraclitus said that fire is the essence of all things. Why?
--shrugs-- Who knows what was in the "Riddler's" head?
The pre-Scoratics, though not as widely studied or influential, are much more in line with modern though than are Plato and Aristotle. They upheld the modern tenets of reductionism and mechanism, something Plato and Aristotle refused to see the beauty in.
For instance, Aristarchus believed the Earth revolved around the sun in an eliptical orbit. Anaximander, as I said above, believed in human evolution for rather ingenius and persipicacious reasons, Eudoxus and Archimedes invented a rudimentary version of calculus 1,000 years before Newton/Leibniz. Eratosthenes made a very accurate trignometric calculation of the Earth's circumference. The list goes on and on. Plato and Aristotle killed this revolution and set back science 2,000 years.