Rust is a young systems programming language designed to provide both the safety guarantees of high-level languages and the execution performance of low-level languages. To achieve this design goal, Rust provides a suite of safety rules and checks against those rules at the compile time to eliminate many memory-safety and thread-safety issues. Due to its safety and performance, Rust's popularity has increased significantly in recent years, and it has already been adopted to build many safety-critical software systems. It is critical to understand the learning and programming challenges imposed by Rust's safety rules. For this purpose, we first conducted an empirical study through close, manual inspection of 100 Rust-related Stack Overflow questions. We sought to understand (1) what safety rules are challenging to learn and program with, (2) under which contexts a safety rule becomes more difficult to apply, and (3) whether the Rust compiler is sufficiently helpful in debugging safety-rule violations. We then performed an online survey with 101 Rust programmers to validate the findings of the empirical study. We invited participants to evaluate program variants that differ from each other, either in terms of violated safety rules or the code constructs involved in the violation, and compared the participants' performance on the variants. Our mixed-methods investigation revealed a range of consistent findings that can benefit Rust learners, practitioners, and language designers.