It's worth noting that "aliasing" in Rust and C typically mean completely unrelated things.
Strict aliasing in C roughly means that if you initialize memory as a particular type, you can only access it as that type or one of a list of aliasable types look like char. Rust has no such restriction, and has no concept of strict aliasing like this. In Rust, "type aliasing" is allowed, so long as you respect size, alignment, and representability rules.
Aliasing safety in Rust roughly means that you can not have an exclusive reference to an object if any other reference is active for that reference (reality is a little bit more involved than that, but not a lot). C has no such rule.
It's very unfortunate that such similar names were given to these different concepts.
No. Aliasing is a single idea, an alias is another name for the same thing. The concept translates well from its usual English meaning.
The C "strict aliasing" rule is that with important exceptions the name for a thing of type T cannot also be an alias to a thing of type S, and char is an important exception. Linux deliberately switches off this rule.
Rust's rule is that there mustn't be mutable aliases. We will see why that's important in a moment.
Aliasing is an impediment to compiler optimisation. If you've been watching Matt's "Advent of Compiler Optimisation" videos (or reading the accompanying text) it's been covered a little bit in that, Matt uses C and C++ in those videos, so if you're scared of Rust you needn't fear that in the AoCO
But why mutation? Well, the optimisations concern modification. The optimiser does its job by rewriting what you asked for as something (possibly not something you could have expressed at all in your chosen language) that has the same effect but is faster or smaller. Rewrites which avoid "spilling" a register (writing its value to memory) often improve both size and speed of the software, but if there is aliasing then spilling will be essential because the other aliases are referring to the same memory. If there's no modification it doesn't matter, copies are all identical anyway.