Fix Emoji-related documentation

* etc/NEWS: Fix wording and spelling.

* doc/emacs/mule.texi (Input Methods): Add index entries and fix
wording.

* admin/notes/unicode: Update instructions for updating Emacs for
the latest Unicode Standard.

admin/notes/unicode

@@ -21,11 +21,14 @@ Emacs uses the following files from the Unicode Character Database
   . emoji-sequences.txt
   . BidiCharacterTest.txt
 
-First, the first 10 files need to be copied into admin/unidata/, and
-the file https://www.unicode.org/copyright.html should be copied over
-copyright.html in admin/unidata (some of them might need trailing
-whitespace removed before they can be committed to the Emacs
-repository).
+Emacs also uses the file emoji-test.txt which should be imported from
+the Unicode's Public/emoji/ directory.
+
+First, the first 10 files and emoji-test.txt need to be copied into
+admin/unidata/, and the file https://www.unicode.org/copyright.html
+should be copied over copyright.html in admin/unidata (some of them
+might need trailing whitespace removed before they can be committed to
+the Emacs repository).
 
 Then Emacs should be rebuilt for them to take effect.  Rebuilding
 Emacs updates several derived files elsewhere in the Emacs source

doc/emacs/mule.texi

@@ -473,6 +473,10 @@ First, letters are mapped into symbols for particular sounds or tone
 marks; then, sequences of these that make up a whole syllable are
 mapped into one syllable sign.
 
+@kindex C-f@r{, when using input methods}
+@kindex C-b@r{, when using input methods}
+@kindex C-n@r{, when using input methods}
+@kindex C-p@r{, when using input methods}
   Chinese and Japanese require more complex methods.  In Chinese input
 methods, first you enter the phonetic spelling of a Chinese word (in
 input method @code{chinese-py}, among others), or a sequence of
@@ -498,6 +502,7 @@ alternatives in the row are also numbered; the number appears before
 the alternative.  Typing a number selects the associated alternative
 of the current row and uses it as input.
 
+@kindex TAB@r{, when using Chinese input methods}
   @key{TAB} in these Chinese input methods displays a buffer showing
 all the possible characters at once; then clicking @kbd{mouse-2} on
 one of them selects that alternative.  The keys @kbd{C-f}, @kbd{C-b},
@@ -571,28 +576,36 @@ modes that make buffer text or parts of it read-only, such as
 @code{read-only-mode} and @code{image-mode}, even when an input method
 is active.
 
+@kindex C-x 8 @key{RET}
+@cindex insert character by name or code-point
   Another facility for typing characters not on your keyboard is by
 using @kbd{C-x 8 @key{RET}} (@code{insert-char}) to insert a single
 character based on its Unicode name or code-point; see @ref{Inserting
 Text}.
 
-@cindex emoji
-  There are specialized commands for inserting emojis, and these can
-be found on the @kbd{C-x 8 e} submap.  @kbd{C-x 8 e e}
-(@code{emoji-insert}) will let you navigate through different emoji
+@cindex emoji input
+@cindex inserting Emoji
+@kindex C-x 8 e
+@findex emoji-insert
+@findex emoji-list
+@findex emoji-search
+  There are specialized commands for inserting Emoji, and these can be
+found on the @kbd{C-x 8 e} keymap.  @kbd{C-x 8 e e}
+(@code{emoji-insert}) will let you navigate through different Emoji
 categories and then choose one.  @kbd{C-x 8 e l} (@code{emoji-list})
-will pop up a new buffer and list all the emojis; clicking (or using
-@kbd{RET}) on an emoji will insert it in the original buffer.
+will pop up a new buffer and list all the Emoji; clicking (or using
+@kbd{RET}) on an emoji character will insert it in the current buffer.
 Finally, @kbd{C-x 8 e s} (@code{emoji-search}) will allow you to
-search for an emoji based on its name.
+search for Emoji based on their names.
 
+@findex emoji-describe
   @code{describe-char} displays a lot of information about the
 character/glyphs under point (including emojis).  It's sometimes
 useful to get a quick description of the name, and you can use the
 @kbd{C-x 8 e d} (@code{emoji-describe}) command to do that.  It's
-meant primarily to help distinguish between different emoji
-derivatives (which can look very similar), but it will also tell you
-the names of non-emoji characters.
+meant primarily to help distinguish between different Emoji
+variants (which can look very similar), but it will also tell you
+the names of non-Emoji characters.
 
 @node Select Input Method
 @section Selecting an Input Method

etc/NEWS

@@ -49,32 +49,32 @@ time.
 ** Emoji
 
 +++
-*** Emacs now has several new methods for inserting emojis.
-The emoji commands are under the new 'C-x 8 e' submap.
+*** Emacs now has several new methods for inserting Emojis.
+The Emoji commands are under the new 'C-x 8 e' prefix.
 
 +++
 *** New command 'emoji-insert' (bound to 'C-x 8 e e' and 'C-x 8 e i').
-This command guides you through various emoji categories and
+This command guides you through various Emoji categories and
 combinations in a graphical menu system.
 
 +++
 *** New command 'emoji-search' (bound to 'C-x 8 e s').
-This command lets you search for emojis based on names.
+This command lets you search for Emojis based on names.
 
 +++
 *** New command 'emoji-list' (bound to 'C-x 8 e l').
-This command lists all emojis (categorised by themes) in a big buffer
-and lets you choose one of them.
+This command lists all Emojis (categorized by themes) in a special
+buffer and lets you choose one of them.
 
 ---
 *** New command 'emoji-recent' (bound to 'C-x 8 e r').
-This command lets you choose among the emojis you have recently
+This command lets you choose among the Emojis you have recently
 inserted.
 
 +++
 *** New command 'emoji-describe' (bound to 'C-x 8 e d').
-This command will tell you the name of the emoji under point.  (This
-command also works for non-emoji characters.)
+This command will tell you the name of the Emoji at point.  (This
+command also works for non-Emoji characters.)
 
 ** Help