I can't remove the demo Welcome page.
It looks like the page is deleted, but immediately a new page (with new content id) is created with the current user as its creator, and root as recent updater of the page.

In Admin > Wiki > Settings, there's a setting for the wiki start page. This is set to "Welcome" by default. For any page name put in there, a page will be created automatically. To change the default start page, you'd have to put the name of your page in there first, and then delete the page "Welcome".

To say what laetzer is saying again... In the wiki settings is a home wiki page option - by default this is "Welcome". If you delete this home wiki page the wiki package will automatically recreate that page next time the 'home' page is requested. Change what you want the home page to be (or it can be a list of wiki pages) and then the Welcome page will not be auto created.

I have named a page in wiki settings, it was created all right, but the links for Wiki in menu continue leading to the list of wiki pages, not to wiki homepage.

I suspect this to be a bug in the current version (2.7), but I might be wrong (didn't investigate this further yet). There could be something wrong with one of the settings in Admin > Wiki > Settings. Seems to me that once a certain setting is set, it changes the default home page of wiki to the page listing and is unable to toggle back to another behavior.

I have the same problem as the above. Whatever changes I do, there is only a list of the wiki pages. Has anyone found a solution or is there a bug fix available?

me too - list of pages. Even through phpmyadmin can't change the settings to show a home page now

fixed mine by going to:
administrative options
Kernel
kernel settings
Configure: Features
Homepage Settings
choosing custom page and adding
index.php?page=Welcome+to+MY+Site (or whatever the page link is)

This bug is fixed in the source code of Bitweaver and will be in the next release. Meanwhile you can use the quick fix mentioned above, or download /wiki/index.php from CVS and replace your local file, or use this code http://paste.pocoo.org/show/162698/ to replace the code in your local file.