The short answers are "probably" and "we don't know".
PIE didn't have quite the same categories of participles that we have today, because its tense-aspect system was very different from English's. (The primary distinction was between perfective and imperfective verbs, like in some Slavic languages today.) And everything we know about it is reconstructed, so there's disagreement about what certain things actually meant.
But *-nt- did create a participle usually described as present active, and *-t- did create a participle usually described as past passive. These are the same participles that survived in Latin: from the stem ama- "love" you get amant- "loving" and amāt- "loved".
As for where they came from…unfortunately, nobody is really sure. PIE is the oldest stage we're able to reconstruct with any certainty. There have been theories proposed about older versions of the language, but none are widely accepted. So PIE is about as far back as you can get.