The snail is a Physa, that doesn't look like one of the species which breeds without control.
I recommend that you get your nitrites into readable territory, as the filter could very well be processing the 14 ppm of nitrite that 5 ppm of ammonia gives within 12 hours. The nitrite reading on day 27 way have been off the scale as for *very* high readings, the water will go purple for a second or so and then the cyan of 0 ppm, even though there is a lot of nitrite in the water.