In this paper, we study the algebra automorphisms and isomorphisms for a family of "symmetric" multiparameter quantized Weyl algebras A q,Λ n (K) and some related algebras in the generic case. First, we compute the Nakayama automorphism for A q,Λ n (K) and give a necessary and sufficient condition for A q,Λ n (K) to be Calabi-Yau. We also prove that A q,Λ n (K) is cancellative. Then we determine the automorphism group for A q,Λ n (K) and its polynomial extension A q,Λ n (K[t]). As an application, we solve the isomorphism problem for {A q,Λ n (K)} and {A q,Λ n (K[t])}. Similar results will be established for the Maltisiniotis multiparameter quantized Weyl algebra A q,Γ n (K) and its polynomial extension A q,Γ n (K[t]). In addition, we prove a quantum analogue of the Dixmier conjecture for a simple localization (A q,Λ n (K)) Z of A q,Λ n (K). Moreover, we will completely determine the algebra automorphism group for (A q,Λ n (K)) Z .