Stealing on catcher's obstruction

ASA Rule 8, Section 1D, EFFECT 3: If all runners, including the batter-runner, do not advance at least one base, the manager has the option to take the result of the play, or have the obstruction enforced by awarding the batter first base and advancing all other runners only if forced.

So, the only way that R1 on 2B can get 3B is by the manager taking the result of the play.

Yes, you are correct about the runner stealing home being awarded home. The batter also is awarded first base on the obstruction.

Hope this answers your questions.