Tested on PS 5.5:

1) 

SHOW CLIENT_STATISTICS like '%localhost%'\G
*************************** 1. row ***************************
                Client: localhost
     Total_connections: 2
Concurrent_connections: 0
        Connected_time: 24
             Busy_time: 0
              Cpu_time: 0
        Bytes_received: 243
            Bytes_sent: 0
  Binlog_bytes_written: 0
          Rows_fetched: 4
          Rows_updated: 0
       Table_rows_read: 0
       Select_commands: 4
       Update_commands: 0
        Other_commands: 1
   Commit_transactions: 0
 Rollback_transactions: 0
    Denied_connections: 0
      Lost_connections: 0
         Access_denied: 0
         Empty_queries: 0
 Total_ssl_connections: 0
1 row in set (0.00 sec)

mysql> SHOW CLIENT_STATISTICS like '%localhost%'\G
*************************** 1. row ***************************
                Client: localhost
     Total_connections: 2
Concurrent_connections: 0
        Connected_time: 122
             Busy_time: 0
              Cpu_time: 0
        Bytes_received: 289
            Bytes_sent: 0
  Binlog_bytes_written: 0
          Rows_fetched: 5
          Rows_updated: 0
       Table_rows_read: 0
       Select_commands: 5
       Update_commands: 0
        Other_commands: 1
   Commit_transactions: 0
 Rollback_transactions: 0
    Denied_connections: 0
      Lost_connections: 0
         Access_denied: 0
         Empty_queries: 0
 Total_ssl_connections: 0
1 row in set (0.00 sec)

mysql> SHOW CLIENT_STATISTICS like '%localhost%'\G
*************************** 1. row ***************************
                Client: localhost
     Total_connections: 2
Concurrent_connections: 0
        Connected_time: 124
             Busy_time: 0
              Cpu_time: 0
        Bytes_received: 335
            Bytes_sent: 0
  Binlog_bytes_written: 0
          Rows_fetched: 6
          Rows_updated: 0
       Table_rows_read: 0
       Select_commands: 6
       Update_commands: 0
        Other_commands: 1
   Commit_transactions: 0
 Rollback_transactions: 0
    Denied_connections: 0
      Lost_connections: 0
         Access_denied: 0
         Empty_queries: 0
 Total_ssl_connections: 0
1 row in set (0.00 sec)


2) 

select * from table_statistics\G
*************************** 1. row ***************************
          TABLE_SCHEMA: mysql
            TABLE_NAME: user
             ROWS_READ: 7
          ROWS_CHANGED: 0
ROWS_CHANGED_X_INDEXES: 0
*************************** 2. row ***************************
          TABLE_SCHEMA: mysql
            TABLE_NAME: proxies_priv
             ROWS_READ: 2
          ROWS_CHANGED: 0
ROWS_CHANGED_X_INDEXES: 0
*************************** 3. row ***************************
          TABLE_SCHEMA: mysql
            TABLE_NAME: db
             ROWS_READ: 2
          ROWS_CHANGED: 0
ROWS_CHANGED_X_INDEXES: 0
3 rows in set (0.00 sec)


mysql> select * from mysql.user\G

.......... 
.........

mysql> select * from table_statistics\G
*************************** 1. row ***************************
          TABLE_SCHEMA: mysql
            TABLE_NAME: user
             ROWS_READ: 14
          ROWS_CHANGED: 0
ROWS_CHANGED_X_INDEXES: 0
*************************** 2. row ***************************
          TABLE_SCHEMA: mysql
            TABLE_NAME: proxies_priv
             ROWS_READ: 2
          ROWS_CHANGED: 0
ROWS_CHANGED_X_INDEXES: 0
*************************** 3. row ***************************
          TABLE_SCHEMA: mysql
            TABLE_NAME: db
             ROWS_READ: 2
          ROWS_CHANGED: 0
ROWS_CHANGED_X_INDEXES: 0
3 rows in set (0.00 sec)





3) 

Regarding "  * Incorrectly counted the kind of queries (Other/Select/etc)" 

the statistics for queries are counted correctly.

However, 

a) CONCURRENT_CONNECTIONS is always zero and is no where updated in the code . It needs to be fixed. 

b) Empty queries doesn't count for queries like 'show global variables like "%... "'