Open and permissionless blockchains are distributed systems with thousands to tens of thousands of nodes, establishing novel platforms for decentralized applications. When realizing such an application, data might be stored and retrieved from one or more blockchains by distributed network nodes without relying on centralized coordination and trusted third parties. Data access could be provided through a query language such as SQL at the application level, establishing a unified view on application-level data that is verifiably stored. However, when accessing multiple blockchains through their node software and APIs, interoperability cannot be assumed today, resulting in challenges of inhomogeneous data access. In addition, different feature sets and trade-offs exist, e.g., regarding smart contract functionality, availability, distribution, scalability, and security. For increasing interoperability, the paper at hand suggests pursuing the development of a cross-chain query language at the application level. The language abstracts from implementation by providing a standardized syntax, an integrated data model, and a processing architecture for data queries. This research is an extended and updated paper of a prior publication demonstrating the language syntax, data model, and architecture with an evaluation of compatibility against the largest open and permissionless blockchains today.