Actually the answer is in the text you posted:


  Normally, all of a player's permanents untap, but effects can keep one or more of a player's permanents from untapping.


So, no, a player cannot chose which permanents to untap during that step, unless an effect  makes it so.

Is untapping my permanents during the untap step optional?
I added this rows to my-default file, restarted server, recreated schema, table and data in the tables, but my cyrillic data still looks like '????'.
Now I have a new user and such config, but utf8 still does not work. 

[mysqld]
init-connect=SET NAMES utf8
character-set-server=utf8
character-sets-dir=/usr/share/mysql/charsets
default-character-set=utf8

[mysql]
character-sets-dir=/usr/share/mysql/charsets default-character-set=utf8

[mysqladmin]
character-sets-dir=/usr/share/mysql/charsets default-character-set=utf8

[mysqlcheck]
character-sets-dir=/usr/share/mysql/charsets default-character-set=utf8

[mysqldump]
character-sets-dir=/usr/share/mysql/charsets default-character-set=utf8

[mysqlimport]
character-sets-dir=/usr/share/mysql/charsets default-character-set=utf8

[mysqlshow]
character-sets-dir=/usr/share/mysql/charsets default-character-set=utf8
#end

