This looks like it's from the Intersection Types portion of the Language Specification. Specifically, the & is an intersection type literal. As for what it does:

Intersection types represent values that simultaneously have multiple types. A value of an intersection type A & B is a value that is both of type A and type B. Intersection types are written using intersection type literals (section 3.8.7).

The spec goes on to offer a helpful snippet to better understand the behavior:

Copyinterface A { a: number }  
interface B { b: number }

var ab: A & B = { a: 1, b: 1 };  
var a: A = ab;  // A & B assignable to A  
var b: B = ab;  // A & B assignable to B

Because ab is both of type A and of type B, we can assign it to a and/or b. If ab were only of type B, we could only assign it to b.

The code you shared may be from this comment on GitHub, which mentions Intersection Types.

Yes. As of TypeScript 3.7 (released on November 5, 2019), this feature is supported and is called Optional Chaining:

At its core, optional chaining lets us write code where TypeScript can immediately stop running some expressions if we run into a null or undefined. The star of the show in optional chaining is the new ?. operator for optional property accesses.

Refer to the TypeScript 3.7 release notes for more details.

Prior to version 3.7, this was not supported in TypeScript, although it was requested as early as Issue #16 on the TypeScript repo (dating back to 2014).

As far as what to call this operator, there doesn't appear to be a consensus. In addition to "optional chaining" (which is also what it's called in JavaScript and Swift), there are a couple of other examples:

• CoffeeScript refers to it as the existential operator (specifically, the "accessor variant" of the existential operator):

The accessor variant of the existential operator ?. can be used to soak up null references in a chain of properties. Use it instead of the dot accessor . in cases where the base value may be null or undefined.

• C# calls this a null-conditional operator.

a null-conditional operator applies a member access, ?., or element access, ?[], operation to its operand only if that operand evaluates to non-null; otherwise, it returns null.

• Kotlin refers to it as the safe call operator.

There are probably lots of other examples, too.

That's the non-null assertion operator. It is a way to tell the compiler "this expression cannot be null or undefined here, so don't complain about the possibility of it being null or undefined." Sometimes the type checker is unable to make that determination itself.

It is explained in the TypeScript release notes:

A new ! post-fix expression operator may be used to assert that its operand is non-null and non-undefined in contexts where the type checker is unable to conclude that fact. Specifically, the operation x! produces a value of the type of x with null and undefined excluded. Similar to type assertions of the forms <T>x and x as T, the ! non-null assertion operator is simply removed in the emitted JavaScript code.

I find the use of the term "assert" a bit misleading in that explanation. It is "assert" in the sense that the developer is asserting it, not in the sense that a test is going to be performed. The last line indeed indicates that it results in no JavaScript code being emitted.