Does God forgive one who falls into blasphemy while believing it to be a whisper from Satan (waswas), and when does a Muslim know that what they are experiencing is a whisper from Satan and not actual blasphemy?

What you have decided concerning turning away from intrusive thoughts is correct, and you must implement it and not pay attention to them. Allah is merciful to His servants and does not hold them accountable for inner speech. All the thoughts that occur in your mind will not be held against you, and none of them constitute mockery that takes one out of the faith.