SET STATISTICS IO- worktable/workfile
1. Why Statistics IO show higher reads than Profiler?

No idea, sorry. There are often differences because they are measuring different things as alluded to in the knowledge base article. There is no additional documentation on this that I am aware of. You might be able to infer some things through detailed testing, but there's really no guarantee whatever you find will remain consistent across versions and builds. The intended behaviour is inconsistent enough, before accounting for possible bugs.

2. What is difference between "Worktable" and "Workfile"

Both are internal objects; otherwise it is pretty much what the names suggest: A work table has a table-like structure, a work file is file-like. The detailed structure is not visible, though some broad features can be discerned by inspecting their methods and following their execution paths with a debugger.

3. Why there is "Worktable" in this particular case?

A work table is always needed for a (row mode) hashing operation. It is used internally in distributing the input into hash partitions (an overloaded term, not related to table partitioning) and to keep track of status. I have never seen a hashing work table report anything other than zero in statistics output, but then I've never really looked into it.

4. What "Physical reads" on Workfile means? 

Work files are part of the mechanism employed when a hash partition spills. Though not documented, the physical and read-ahead reads occur when the execution engine retrieves spilled hash partitions from the work files.

5. One "workfile" means exactly one table that is used for one purpose?

As I recall, there may be multiple instances. There is no way I know of to relate a particular STATISTICS IO line to a particular object or plan node. This is a long-standing limitation. There may be a change to this in SQL Server 2016, though I have not tested to see if it applies to internal temporary objects.

Ultimately, there's not that much useful to be learned from STATISTICS IO output for work files and work tables beyond that which you can learn by looking at other information in a post-execution plan (or via DMVs, Extended Events etc.). I apologise for the incomplete answer, but it's the best I can offer off the top of my head.