Weird toilet leaks

So my toilet started leaking from the base, so I turned the water off and took the toilet apart. The lip of the flange had broke and the wax ring was gone. Replaced the lip with a metal replacement plate, put quick Crete around flange so that we could have something to drill the bolts into something to hold the plate. Replaced bowl on new wax ring, and it holds water, no apparent leaks. Replaced tank – when my dad did this, he let water get all over the floor, then downstairs neighbor complained of water coming out of their bathroom ceiling vent/fan. I freaked out and stopped working on it.

Months later, bowl still is holding water, and no complaints of leaking downstairs, so I replaced the tank myself. A small amount of water got on the floor but I was very careful. Then I got the toilet operational. Yay! But then neighbor came upstairs screaming about the water out of her vent again.

There is a space between where the toilet meets the tile. Could this be the cause of the leak she is seeing out of her bathroom vent?

Pics of the gaps:

I market the water line with a marker hours ago, and the water is holding