Is it possible to say 2,3? I don't think so. I think where should be changed to which.
1.Sit where you like.
2. Sit on the chair where you like => which
3. Sit at the table where you like.=> which
The most natural sentences are (1) and (2) with 'where'.
.. "wherever" and "whichever" are quite common in this situation, they emphasize the lack of restriction within the options provided, in this case a table surrounded by chairs.
These work OK:
Sit where/wherever you like.
Sit at the table wherever you like.
Take whichever chair/place you like.
.. and of course there are others.
not a teacher
Student or Learner