My first plugin doesn’t save the data in options

The problem is your validate function RSP_options_validate(). This function always a empty string. Check your conditional statement with preg_match.

If you test your source without this functions, it works.

register_setting( 'RSP_options_group', 'RSP_options', 'RSP_options_validate' );

to

register_setting( 'RSP_options_group', 'RSP_options' );