A: Yes, although a bit cryptic:

• ADConnection1.ConnectionIntf.Driver.CliObj - returns reference to TMySQLLib;
• ADConnection1.ConnectionIntf.CliObj - returns reference to TMySQLSession, which has MySQL property;
• alltogether:

uses
  uADPhysMySQLCli, uADPhysMySQLWrapper;
...
  with ADConnection1.ConnectionIntf do
    TMySQLLib(Driver.CliObj).mysql_thread_id(TMySQLSession(CliObj).MySQL);

A: Please, check: http://dev.mysql.com/doc/refman/5.0/en/gone-away.html and at first the item, which suggest to increase max_allowed_packet. 

A: Yes, it is possible. For that set UseSSL=True for a connection definition. Then specify SSL_key, SSL_cert, SSL_ca, SSL_capath and SSL_cipher parameters. For the parameters meaning, please, read: http://dev.mysql.com/doc/refman/5.1/en/ssl-options.html. Note, that you can also use the my.cnf configuration file. 

A: If your application creates threads, this issue (AD-58) is possible with libmysql.dll v 5.x. Please, read http://bugs.mysql.com/bug.php?id=37226 for details. As workaround try to terminate all threads before terminating the application.