Add C document to sphinx, fix arrow. (#8300)

- Group C API.
- Add C API sphinx doc.
- Consistent use of `OptionalArg` and the parameter name `config`.
- Remove call to deprecated functions in demo.
- Fix some formatting errors.
- Add links to c examples in the document (only visible with doxygen pages)
- Fix arrow.

doc/Doxyfile.in

@@ -753,7 +753,7 @@ WARN_LOGFILE           =
 # spaces.
 # Note: If this tag is empty the current directory is searched.
 
-INPUT                  = @PROJECT_SOURCE_DIR@/include @PROJECT_SOURCE_DIR@/src/common
+INPUT                  = @PROJECT_SOURCE_DIR@/include
 
 # This tag can be used to specify the character encoding of the source files
 # that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses
@@ -822,7 +822,7 @@ EXCLUDE_SYMBOLS        =
 # that contain example code fragments that are included (see the \include
 # command).
 
-EXAMPLE_PATH           =
+EXAMPLE_PATH           = @PROJECT_SOURCE_DIR@/demo/c-api/
 
 # If the value of the EXAMPLE_PATH tag contains directories, you can use the
 # EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp and
@@ -836,7 +836,7 @@ EXAMPLE_PATTERNS       =
 # irrespective of the value of the RECURSIVE tag.
 # The default value is: NO.
 
-EXAMPLE_RECURSIVE      = NO
+EXAMPLE_RECURSIVE      = YES
 
 # The IMAGE_PATH tag can be used to specify one or more files or directories
 # that contain images that are to be included in the documentation (see the
@@ -1934,7 +1934,7 @@ ENABLE_PREPROCESSING   = YES
 # The default value is: NO.
 # This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
 
-MACRO_EXPANSION        = NO
+MACRO_EXPANSION        = YES
 
 # If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES then
 # the macro expansion is limited to the macros specified with the PREDEFINED and
@@ -1942,7 +1942,7 @@ MACRO_EXPANSION        = NO
 # The default value is: NO.
 # This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
 
-EXPAND_ONLY_PREDEF     = NO
+EXPAND_ONLY_PREDEF     = YES
 
 # If the SEARCH_INCLUDES tag is set to YES the includes files in the
 # INCLUDE_PATH will be searched if a #include is found.
@@ -1974,7 +1974,9 @@ INCLUDE_FILE_PATTERNS  =
 # recursively expanded use the := operator instead of the = operator.
 # This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
 
-PREDEFINED             = DMLC_USE_CXX11
+PREDEFINED             = DMLC_USE_CXX11 \
+                         "XGB_DLL=" \
+                         "XGB_EXTERN_C="
 
 # If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then this
 # tag can be used to specify a list of macro names that should be expanded. The