Hi

Problem is that actually I deleted all blogs from the Community Web Site manually, because I wanted to evaluate how 1 blog will work on a free edition. And as far as there was a licensing problem I had to delete all blogs manually

See related post here

Finally I created a new blog from CMS desk

What is interesting, I can't find what settings is responsible in What tag group will be inserted new tags for new blog posts?
See, when I adding a new blog post with a new tag, "newtag", I see in SQL Profiler, that it executes a query (I will post only the query related to "newtag" )

exec Proc_CMS_DocumentTag_AddTag @TagName=N'newtag',@DocumentID=207,@TagGroupID=2

When I look to the CMS_TagGroup, I see here

select TagGroupID, TagGroupName, TaggroupSiteID from dbo.CMS_TagGroup

TagGroupID  TagGroupName TaggroupSiteID
----------- ------------ --------------
1           content      1
2           content      2
3           News         2
4           Blogs        2

so, @TagGroupID=2 refers to TagGroup = "content"

That is why when I adding new blog posts, the tags for new posts appear to belong to "content" tag group, but not to the "blogs"

Again, may be you are right and some my settings is wrong, or maybe your code doesn't take into account the case when I manage more then one site
I don't know, but I suppose that if you have access to the source code, you can quickly debug to the line, where procedure Proc_CMS_DocumentTag_AddTag is being executed, and see, what parameter it takes for @TagGroupID