Several well-studied online resource allocation problems can be abstracted in terms of an infinite, increasing sequence, where each element is associated with a corresponding allocation value. In Theoretical Computer Science, one such abstraction is known as online bidding, in which an algorithm must submit "bids" until an unknown threshold is reached. Another abstraction that has been studied extensively in Artificial Intelligence is known as contract scheduling: in this formulation, an algorithm is repeatedly executed with increasing processing times so as to obtain a system with interruptible capabilities. We study such problems under the query prediction model, in which the designer elicits a prediction on the instance via responses to k binary queries so as to improve the algorithm's performance. The queries are answered by an imperfect oracle, and the objective is to obtain efficient algorithms that are robust to query errors. We first focus on {\em consistency-robustness} tradeoffs, in which the query responses are either error-free or are generated by a (malicious) adversary: here, we prove a tight information-theoretic lower bound that establishes {\em Pareto-optimality} with respect to the consistency and the robustness. Next, we consider the more general setting in which some of the query responses can be erroneous: here, we present and analyze an efficient and robust algorithm based on {\em adaptive} queries. Specifically, we show that small increments in the number of queries lead to substantial improvement in robustness to query errors, in that the performance of our solution approaches the ideal performance of the Pareto-optimal schedule very quickly as $k$ grows, even if as many as $k/4-o(k)$ responses are adversarially erroneous. Our techniques have applications outside the query model: Namely, we show how to obtain an optimal schedule for a generalization of the {\em fault tolerant} contract scheduling problem in a multi-processor system, which generalizes the setting of [Kupavskii and Welzl, {\em Distr. Comp.} 2019].