Will a rusty tool or bolt lying with other tools or bolts induce them to rust as well?
Rust is not mould, rust is oxidization of the metal and cause by the oxygen in the air.

Most tools, nuts and bolts have a rust proofing in the form of a light coating of oxidization (often of a metal that's not iron) that will isolate the material underneath from further rust. A scratch in that coating will then let the rust spread again.

For long term storage you can oil the tools.