There are many reasons why Atatürk decided to use the Latin alphabet. I shall take the three points in your question:
1. The official language of the Ottoman Empire was Ottoman Turkish, a language that contained many Arabic and Persian loanwords. This was far removed from how most people actually spoke. The language revolution in Turkey was an attempt to purify the Turkish language of these loanwords and to replace them either with genuine Turkish words (öztükçe) or with words created from Turkish roots and derived according to the logic of the Turkish language. Motivations behind this would have included creating a new national language for a new nation state and distancing the Turkish Republic from the Ottoman Empire.
2. The Latin alphabet does meet the demands of the Turkish language far better than the Arabic alphabet. As you know, the Arabic alphabet does not normally write short vowels, and while this is suitable for Arabic, where most of the short vowels are predictable either from the form of the word or from the context of the sentence, this is not the case for Turkish. Standard Arabic orthography recognises six vowels, three short and three long (according to most interpretations - a more traditional interpretation would be three vowels and three semi-vowels, "letters of prolongation"), whereas native Turkish words have eight different vowel sounds, all of them short. (Long vowels in Turkish, sometimes marked with a circumflex, are found exclusively (?) in loanwords from Arabic and Persian.) Just as the Turkish vowel system cannot be expressed in an unambiguous way in the Arabic alphabet, the Turkish consonant system was not - until the very end of the Ottoman Empire - able to be accurately represented, at least according to the usual Ottoman orthography; a good example of this would be the letter "kaf" which was could be used to represent "k", "g" and, on occasion, "n" (when it was derived from "ñ").