Does anonymous can access current node? How to check it in my module? I need to do something witn current node by my module only if anonymous users can view this node. How to check it?

By default I use $node-&gt;status == 1, but some other modules can change anonymous access rights also for published nodes.
Also, for development especially, Devel module's Devel Node Access submodule provides a block that you can display that shows, on any given content page, all the user access permissions/grants provided, and even displays a few users and the access they would be given if they tried accessing the page, editing, deleting, etc.

Check it out: http://drupal.org/project/devel

Also, just a short bit ago, Larry Garfield posted an excellent overview of node access in Drupal 7 (applies almost without any adaptation to the Drupal 6 systems as well).