Yes, there are chances of water penetration at the edges. The plasterer should have covered these gaps to prevent water seeping in behind. Ask them to reconsider the rendering as it is not done according to the requirement.
I think yes, you can build a free standing solid wall with a end pier. In order to overcome with the gap problem, I think you need expert advice. Get in touch with a professional in your neighborhood and understand the actions required.
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Obviously it will affect a effectiveness of the insulation. In addition to this, it can destroy the appearance as well. If it is a new house as you mentioned in your question, there is no need to add loft boards to the joists.
