Can I disable rating for all albums (including newly created one) by default and set rating permission to one or two albums later on?
Yes.
I heard I can do this by modifying MySQL database, but I don't know how.
Sort of yes - you need to run a query on the database (using phpMyAdmin or similar). Your query should look like this:
ALTER TABLE `YourCoppermineTablePrefix_albums` CHANGE `votes` `votes` ENUM( 'YES', 'NO' ) NOT NULL DEFAULT 'NO'
This will set the default for rating to 'NO' for newly added albums. However, fiddling with the database can be tricky if you don't know your way around - I don't recommend doing this if you're not absolutely sure what you're doing.
Another option would be to modify the query within delete.php that creates new albums, the corresponding line in delete.php is
$query = "INSERT INTO {$CONFIG['TABLE_ALBUMS']} (category, title, uploads, pos) VALUES ('$category', '" . addslashes($op['album_nm']) . "', 'NO', '{$op['album_sort']}')";
which should be replaced with
$query = "INSERT INTO {$CONFIG['TABLE_ALBUMS']} (category, title, uploads, pos, votes) VALUES ('$category', '" . addslashes($op['album_nm']) . "', 'NO', '{$op['album_sort']}', 'NO')";
(not tested though, please report if this works for you). Again, this applies to new albums you create from now on. Your old (existing) albums will remain as they are, either use Coppermine's user interface (album properties) to change the ability to rate one by one. If you feel adventurous, you could come up with a query (to be run in phpMyAdmin) that sets all existing albums to "no rating".