For any linear k-uniform F, we provide a bound on alpha = alpha(n) in terms of p = p(n) and F, such that (under natural divisibility assumptions on n) any k-uniform (p, alpha, o(1))-pseudo-random n-vertex hypergraph H with a mild minimum vertex degree condition contains an F-factor. The approach also enables us to establish the existence of loose Hamilton cycles in sufficiently pseudo-random hypergraphs and, along the way, we also derive conditions which guarantee the appearance of any fixed sized subgraph. All results imply corresponding bounds for stronger notions of hypergraph pseudo-randomness such as jumbledness or large spectral gap. As a consequence, (p, alpha, o(1))-pseudo-random k- graphs as above contain: (i) a perfect matching if alpha = o(p(k)) and (ii) a loose Hamilton cycle if alpha = o(p(k-1)). This extends the works of Lenz-Mubayi, and Lenz-Mubayi-Mycroft who studied the analogous problems in the dense setting.