1) One who is sitting during prayers, may not be stringent and stand when he reaches the Shema, as the law is that one may read the Shema even when sitting (Shulchan Aruch and Mishne Berurah 61). If he is standing to concentrate better or to avoid falling asleep, there are those who forbid it (Mishne Berurah ibid) and others permit it (Ben Ish Chai Vaera 15). If he was already standing, he is permitted to remain standing while reciting the Shema. It is, however, better to sit while reciting the Shema, both according to the revealed and hidden parts of the Torah. (Peri Megadim and Ben Ish Chai)
2) Even though one may recite the Shema while walking, ideally one should stop walking while reciting the first verse of the Shema so that he can concentrate properly. He should also remain stationary for the verse “Baruch sheim”, and others say that he should not continue walking until the words “Bechal levavecha”, and from then onwards he may continue walking. (ibid)