Is Solidity being replaced by languages such as Rust or other programming languages for smart contract development?
Ethereum blockchain's smart contracts run on a specific type of bytecode. Solidity is one of the languages with which you can produce the required bytecode - another option being Vyper (also some other small partially forgotten languages).
The reason you can't use other languages (such as Rust) currently is that you can't produce the required bytecode from those languages. There simply aren't compilers for that. There have been various attempts of compiling various common langauges into Ethereum bytecode but with not much success.
With Eth2.0 the blockchain plans to migrate from the Ethereum bytecode usage (EVM) into using WebAssembly (EWASM). Here's some more info about that: https://medium.com/chainsafe-systems/ethereum-2-0-a-complete-guide-ewasm-394cac756baf
At that point WebAssembly becomes probably the de facto standard for smart contracts, but there's no way to be sure. Possibly Solidity will exist alongside.