1
There's a big difference if you don't await the Task or you await it:
Case you don't await it: DoSomething is called but next sentence is executed while DoSomething Task hasn't been completed.
Case you await it: DoSomething is called and next sentence is executed once DoSomething Task has been completed.
So, the need of async/await will depend on how you want to call DoSomething: if you don't await it is like calling it the fire & forget way.
2
Is it running on the main UI but on a separate thread or is it running on a seperate thread and separate is asynchronously inside that method?
Asynchronous code sometimes means other thread (see this Q&A Asynchronous vs Multithreading - Is there a difference?). That is, either if the code is being executed in a separate thread from the UI one or it lets continue the processing of the UI thread while it gets resumed, it's nice because UI loop can still update the screen while other tasks are being done in parallel without freezing the UI.
An asynchronous method (i.e. async method) is a syntactic sugar to tell the compiler that await statements should be treated as a state machine. The C# compiler turns your async/await code into a state machine where code awaiting a Task result is executed after the code that's being awaited.
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OP said...
[...] But does this mean that "async/await" will fire off a thread and Task.Run also fires off a thread or are they both the same thread?
Using async-await doesn't mean "I create a thread". It's just a syntactic sugar to implement continuations in an elegant way. A Task may or may not be a thread. For example, Task.FromResult(true) creates a fake task to be able to implement an async method without requirement it to create a thread:
public Task<bool> SomeAsync() { // This way, this method either decides if its code is asynchronous or // synchronous, but the caller can await it anyway! return Task.FromResult(true); }
await, but don't doTask.Run.]