[docs/api] Minor adjustments and fixes to api.dart.dev homepage

- Since "Futures", "Streams", and "Zones" are plural and not in code syntax, can make them lowercase to be consistent with the `dart:core` entry in the same list.
- Use the full "platform interopability" term when introducing the libraries, as it might be a newer term for readers.
- Replaces "interoping" term as after searching it seems not common and easily mistaken.
- Fixes spelling of "function"

Change-Id: Ia887b427789a50d70cb47228c677fe2fd03499e2
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/349421
Reviewed-by: Kevin Moore <kevmoo@google.com>
Commit-Queue: Kevin Moore <kevmoo@google.com>
Reviewed-by: Marya Belanger <mbelanger@google.com>
diff --git a/sdk/api_readme.md b/sdk/api_readme.md
index f95e420..9ec2b66 100644
--- a/sdk/api_readme.md
+++ b/sdk/api_readme.md
@@ -7,16 +7,18 @@
     strings, numbers, collections, errors, dates, and URIs.
   * [dart:io](dart-io/dart-io-library.html): I/O for non-web apps.
   * [dart:async](dart-async/dart-async-library.html): Functionality for
-    asynchronous programming with Futures, Streams, and Zones.
+    asynchronous programming with futures, streams, and zones.
 
-You'll also find reference documentation covering Dart's various interop options,
-such as:
+You'll also find reference documentation covering Dart's
+various platform interoperability options, such as:
 
-  * [dart:js_interop](dart-js_interop/dart-js_interop-library.html): Library including
-    a sound type hierarchy and helper functions for interoping with JavaScript.
-  * [package:web](https://pub.dev/documentation/web): DOM manipulation for web apps.
-  * [dart:ffi](dart-ffi/dart-ffi-library.html): Foreign funtion interfaces for
-    interoping with the C language.
+  * [dart:js_interop](dart-js_interop/dart-js_interop-library.html):
+    Library including a sound type hierarchy and helper functions
+    for interoperability with JavaScript.
+  * [package:web](https://pub.dev/documentation/web):
+    DOM manipulation for web apps.
+  * [dart:ffi](dart-ffi/dart-ffi-library.html): Foreign function interfaces for
+    interoperability with the C language.
 
 The core libraries - except for `dart:core` - must be imported before they're
 available for use:
@@ -34,7 +36,7 @@
 
   * [Dart overview](https://dart.dev/overview)
   * [Dart language documentation](https://dart.dev/language)
-  * [Library tour](https://dart.dev/guides/libraries/library-tour)
+  * [Library tour](https://dart.dev/libraries)
   * [Tutorials](https://dart.dev/tutorials)
 
 This API reference is generated from the SDK source at