I would formulate this a bit milder: many desktop applications are written in C++ and many system applications (e.g. UNIX command-line tools) could be written in Swift or Go. So, there are certainly areas where C++, Rust, Go, and Swift are or will be in competition.
Of course, if you require strong safety guarantees and the absence of a garbage collector, Rust is probably the only modern option.
No, it's optional if you don't need to interact with Obj-C frameworks (ie. Cocoa). And memory is not managed dynamically. Swift uses ARC.
Like I said, I just don't see Rust sticking around for long. Swift will suck all the developers out of it since you'll be able to actually get a job programming in Swift.
If anything, Rust is the only modern language that's not threatened by Swift, by virtue of existing at a level of the stack that's so low as to be out of Swift's reach. I agree that Swift is going to be huge, but you're mistaken as to who its competitors are. :P
Rust provides dynamic memory management too, but you aren't forced to use it and most use it for a few variables only.
So far nothing I've seen about Swift tells me that it will be able to be used for things like Servo and other perf-critical applications. Yes, it might edge out Rust webdev, but not much more.
"You cam get a job in swift" is largely due to its iOS backing. I'm not so sure how that's going to apply to other OSs especially if Cocoa and co aren't made open source.
let foo = Moves::new();
if condition { mem::drop(foo) }
// should foo be dropped here?
Swift isn't going to penetrate to the bottom of the stack with pervasive reference counting. You'd either have to start managing memory manually (as per C) or implement a borrow checker (as per Rust), and even then your entire ecosystem is still going to use reference counting pervasively due to the language's defaults. One of the benefits of Rust defaulting to linear types and borrowed references is that it creates an entire package ecosystem where dynamic memory management is the exception, not the rule.
For the record, I think Swift is super fantastic as a language and I'm thrilled that it's going open-source. I think the two languages will work swimmingly together. :)