In a recent survey (Drewes, 2017) of results on DAG automata some open problems are formulated for the case where the DAG language accepted by a DAG automaton A is restricted to DAGs with a single root, denoted by L(A)u. Here we consider each of those problems, demonstrating that: (i) the finiteness of L(A)u is decidable, (ii) the path languages of L(A)u can be characterized in terms of the string languages accepted by partially blind multicounter automata, and (iii) the Parikh image of L(A)u is semilinear.