Perhaps you enter it with a space, which is not allowed. You can use only digits, letters and hyphens.

Is it possible to display in messages and statistics not only a username (link), but also a small image of the size of a username?

It is hardly possible. It is very difficult and time-taking.

Many users come to the site from the same IP. Now they can't authorize themselves on the site. How can I fix it?

Check permissions of user groups, particularly session binding to IP: Main page » Users » User groups » Edit group properties or permittions: Bind session to IP address (protection from stealing cookies). Disable this option.

What should I write in the code to display last user's visit?
How can I specify near a username duration of last visit to the forum?

It is not possible to implement. If you really want it, write this time in cookies, and then read it. Then there will be load not on the server but on users' computers...

There are two administrators on the site. One of them cannot change the password of the other: "You are trying to do illegal action!". What is the reason?

Administrator must change the password himself. It is not allowed to edit administrator's account.

What does "Checked users" mean?

Every site administrator can make users CHECKED at his own discretion and assign to them any permissions he wants. You may set group permissions as you wish. So, groups (or members) will differ on the permissions that you have assigned to them. In this forum a checked member does not have to enter security code.

Is it possible to allocate and change disk space quotas for users?

No.

What should I change in settings so that an administrators didn't have to check and activate all new entries, added by users?

Disable pre-moderation. Control Panel >> Users >> User groups.

Two users on my site have the same IP address. I want to ban one of them, not both! What should I do?

Ban not by IP, but by username.

Is it possible to do the following: a user cannot see a certain post in the forum if he/she has less than 10 posts?

No. Ability to see or not to see posts and certain forums depends on group permissions, not on user's activity.

I've created a group with administrator permissions. But if a user of this group enters user's profile, there is no link for editing or removing a user. How can I create such control elements for this group?

Only one group can have true administrator permissions - Administrators group, which is original, not a created one.

Is possible to make a many-colored username, e.g.: Medved

It is impossible with a script that makes it universally. Username is stored in the database as a whole, so it can be colored "on fly" only. Besides, you don't know how different browsers will react to it...

Is it possible to make user's profile page a common page, not a pop-up window?

Yes. Edit template of user's profile page.

Entries of a removed user a saved and he/she is marked there as an author. What will happen with this authorship if a user with the same username register?

It will be a new user.

Is it possible to remove security code for guests in Site Catalog (Publisher, News etc.)?

It is impossible to remove security code for guests in any module. It is the protection against spam.

For all other groups security code can be disabled in group settings. The code is disabled by default for moderators and administrators.

Is it possible to change the "design" of image with the code? I often confuse digits (especially 3 and 8, 6 and 5).

No, a user cannot change this parameter. Image complexity was increased because of users' complaints, that some programs could read the previous variant and therefore spammed Guestbooks and Site Catalogs. So, such images will remain as they are in the nearest future.

Where can I activate the following feature - I press the link to user's entries, go to that page and there is the inscription

This feature is not activated by the site administrator.

This feature can be activated in fine settings of each module. It is called Enable capability to search entries of a particular user (check it).

It is possible to assign an ordinary user the permission to edit own posts without (!) the inscription "edited by" till the first answer to this post?
And the same concerning removal of own posts...

No, an ordinary user cannot do this. This enhanced feature of threads and posts management is available only for the groups with this option enabled in permissions.

You can remove this inscription for the whole group or for all groups by means of editing the template of messages appearance.

Only administrators, moderators and the groups with this option enabled can remove messages.

I close a thread.... but ordinary users can still leave there posts, what should I do?

If a user had a reply form opened before you closed the thread, then he/she may leave 1 message. But only such users.

There is the following message for guests on the catalog main page:
"You have no permission to view entries."
The appropriate parameters are enabled in settings:
"View catalog Users, Checked, Moderators, Administrators, Guests
Add entries Users, Checked, Moderators, Administrators, Guests
Follow links Users, Checked, Moderators, Administrators, Guests"

What's wrong?

Entries can be unchecked and visible only for the administrator or a user who has the right to manage entries. The prohibition may be also set directly in categories. (Entries and categories management).