My tenant built shelving and re-tiled a bathroom. Whose is it?
Fixed improvements generally become part of the building, so they are yours at the end of the tenancy. The insurance question is whether your dwelling limit reflects the property as it now stands, because a meaningful alteration raises what rebuilding costs.
They did electrical work themselves. Should I worry?
Yes. Unpermitted electrical or plumbing work is a hazard in a building you own, and if it causes a loss the quality of that work becomes central. It is worth inspecting and, where necessary, having it corrected by a licensed contractor.
How do I stop this happening?
A lease clause setting out what requires written permission and what happens at the end of the tenancy. It costs nothing, it prevents most disputes, and it gives you a basis to insist work is done properly.