Water appearing at base of toilet.

You should check is the water coming from the inlets under the cistern, or from the entries into the toilet pan (i.e. the junction of the soil pipe, or the flush pipe). A good clue would be to dry all the areas up and leave the toilet unused for a few hours, if the water is constantly reappearing, then it is most likely the cistern. If the water only appears when the toilet is used, then it is most likely the Soil or flush pipe connections.

Could be loads of things. Wipe all pipes dry then spend some times touching around water inlet and soil pipe. If all dry after an hours or so flush and recheck. Another strange issue i found somewhere is a serious case of condensation when they were having a shower. The condensation would of former on the cistern and pan, then water would slide down on the floor at the base of the pan, forming a little puddle.

This could be a simple washer on the cistern that is leaking down to the pan or it could be a leak on the pan WC outlet