Problem Statement

Find the character and byte length of a string. This means encodings like UTF-8 need to be handled properly, as there is not necessarily a one-to-one relationship between bytes and characters. By character, we mean an individual Unicode code point, not a user-visible grapheme containing combining characters. For example, the character length of "møøse" is 5 but the byte length is 7 in UTF-8 and 10 in UTF-16. Non-BMP code points (those between 0x10000 and 0x10FFFF) must also be handled correctly: answers should produce actual character counts in code points, not in code unit counts. Therefore a string like "𝔘𝔫𝔦𝔠𝔬𝔡𝔢" (consisting of the 7 Unicode characters U+1D518 U+1D52B U+1D526 U+1D520 U+1D52C U+1D521 U+1D522) is 7 characters long, not 14 UTF-16 code units; and it is 28 bytes long whether encoded in UTF-8 or in UTF-16.
Please mark your examples with ===Character Length=== or ===Byte Length===. If your language is capable of providing the string length in graphemes, mark those examples with ===Grapheme Length===.
For example, the string "J̲o̲s̲é̲" ("J\x{332}o\x{332}s\x{332}e\x{301}\x{332}") has 4 user-visible graphemes, 9 characters (code points), and 14 bytes when encoded in UTF-8.

Let's start with the solution:

/*REXX program displays the lengths  (in bytes/characters)  for various strings.        */
    /*            1         */                         /*a handy-dandy over/under scale.*/
    /*   123456789012345    */
hello = 'Hello, world!'      ;        say  'the length of HELLO is '   length(hello)
happy = 'Hello, world! ☺'    ;        say  'the length of HAPPY is '   length(happy)
jose  = 'José'               ;        say  'the length of  JOSE is '   length(jose)
nill  = ''                   ;        say  'the length of  NILL is '   length(nill)
null  =                      ;        say  'the length of  NULL is '   length(null)
sum   = 5+1                  ;        say  'the length of   SUM is '   length(sum)
                                                       /*   [↑]  is, of course,  6.     */
                                                       /*stick a fork in it, we're done.*/