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Floor joists typically 'stagger' half way onto a central bearing beam.
Depending on the span, species of lumber, whether they are true 2"x8" joists, and their spacing on center...your current joists can be entirely acceptable for your floor load needs.
Likewise, if your 'front' and 'back' walls are not load bearing, it shouldn't much matter if there is any daylight at the point they join the foundation since there are no loads being transferred here.
Please describe in detail what you are seeing. For the moment I see no problem.