Well, I would say sometimes there is a difference: חָפֵץ are often artifically made things, objects of your desire, you can buy in a store, gadets and the clutter of things I have on my desk, whereas objects of the natural world, let's say an asteroid in space, are עֶ֫צֶם.
Well, for such question you have to compare the other semitic languages too, and Ugaritic, Phoenician and Arabic, Ethiopian and Akkadian too have variations of עץ, all meaning "tree" or "wood" with two radicals, but the root-family עצם is attested in verbal and nominal forms in Phoenician, Ugaritic and Arabic. There is no usual development or any indication, that these words have interacted.
Well, א was the letter used for a weak guttural, the glottal stop, like in English to separate vowels (uh-oh!) or in Cockney English boʾʾle. It always became silent if closing a syllable, but was retained in spelling here, when prebiblical hūʾa (whose reflex הואה is still visible in Qumran Hebrew next to הוא and הו) lost its final vowel. Sometimes אָלֶף now helps to distinguish homophones (לֹא not, but לוֹ him) or different verb conjugations (מָצָא find, but בָּנָה build). It is dropped in some compound words, so you write מַ֫שֶּׁהוּ something, although it is formed from מַה־שֶּׁ־הוּא.
Well, I suppose the scrolls of Qumran are not your main reading material. For example 4QDª 11,9: ואמר ברוך את אונ הו הכול ובידיך הכול ועושה הכול אשר יסדתה ...saying Blessed are you, vigour, who is everything, in your hands is everything, you do everything, you have founded... Note the use of אוֹן as a replacement for the divine name. Still more often the form אפהו even he is used in Qumran.