Hi unveiledartist. I’m trying to grok your question here, so let’s work it out.
Rather than saying “kept”, I would phrase it rather as “actions have an ongoing influence on consciousness”. It’s true, some Buddhist traditions used the concept of a “storehouse” to explain this, but I don’t feel that’s the most useful metaphor. Better think of it like a stream: you dump pollution in a stream, it will make its toxic effects known downstream (i.e. later in this life or in future lives) until it’s either diluted or cleaned up.
That’s right. But it’s complicated; we do many actions of many different sorts, so rebirth may be conditioned by all sorts of things.
I don’t think there’s anything exactly like that in the suttas. They don’t really have a term of “subconscious” or “unconscious”. Rather, they speak of the “stream of consciousness”. But of course, due to ignorance we are often unaware or deluded about what is going on in consciousness. This is not really all that different to the western idea of subconsciousness, but it’s just a different way of talking about it.
Does that help?