What penalty should the Dummy receive for telegraphing to his partner after play has started?
According to the Laws of Duplicate Bridge (2008), the specific Rights and Limitations of Dummy are listed as Laws 42 and 43. Notable limitations in this context are:


  Law 43
  DUMMY'S LIMITATIONS
  Except as Law 42 allows:
  A. Limitations on Dummy     ...
     1. (c) Dummy may not participate in the play, nor may he communicate anything about the play to declarer.
  ...
   2. (c) Dummy may  not, on his own initiative, look at the face of a card in either defender's hand.  
  
  B. If a Violation Occurs
  1. Dummy is liable to penalty under Law 90 for any violation of the limitation listed in A 1 and A2 above.
  ...
  LAW 90
  PROCEDURAL PENALTIES
  A. Director's Authority
  The Director, in addition to implementing the rectifications in these laws, may also assess procedural penalties for any offense that unduly delays or obstructs the game, inconveniences other contestants, violates correct procedure, or requires the award of an adjusted score at another table.


Additionally Law 45 F states:


  F. Dummy Indicates Card
  After dummy's hand is faced, dummy may not
  touch or indicate any card except for purposes of arrangement, without
  instruction from declarer. If he does so, the Director should be
  summoned forthwith and informed of the action. Play continues. At the
  end of play the Director shall award an adjusted score if he considers
  the dummy suggested a play to declarer and the defenders were damaged
  by the play suggested.


In a duplicate game, if a dummy at my table touched any ,in any manner other than to play a card indicated by declarer by name or to mark tricks in the prescribed fashion, I would immediately call Director for protection. I want the action to stop and to not be resumed, and the appropriate way to do that is to call Director.  

As described by you, both instances of dummy's behaviour are in my opinion clearly in violation of Law 43 A 2 (c). As A Director, I would award an adjusted score (under Law 45 F) if there was the reasonable possibility that damage occurred by any play that might have been suggested by dummy's action. I would then give a stern warning to both members of the offending partnership, and (except for novices), assess an additional half board penalty (under Law 90 A) to the offending player. A repeat occurrence by either member of that partnership in that game would get the offending player an additional full board penalty (again under Law 90 A).