Dear Rabbi, Is it a Minhag or a Halachic requirement to cover the Shel Yad with a shirt sleeve or coat sleeve when davening? And, if it is minhag, whose Minhag is it [e.g. Chassidus, Litvak, etc]?

According to the Shulchan Aruch there is no requirement to cover the Shel Yad at all (OC 27,11 in the Remah). However, later authorities ruled that it is proper to cover the Shel Yad (Mishna Berura 47). The Levush saw an indication to this in the verse "It shall be a sign to you on your hand" (Sha'arei Teshuva). The Kabbalists are very strict about covering the Shel Yad and hide the Shel Yad even when they are tying it on (Sha'arei Teshuva). See also Ben Ish Chai (Parashat Vaera 16). Rabbi Baruch Paz