IMHO no to both questions. Keep it in a sunny window until all danger of frost are past (mid-late May), then put out side in full sun all day. Your aquarium water is probably from your tap so that's a no no too. Distilled or rainwater only.

Aquarium water also has its ph all wrong, the nitrates and nitrites boosted (ammonia is also high), as fish have been living in it for too long. Bacteria and waste accumulate in such tanks, making the results a high grade of fertilizer that would basically kill your Flytrap faster than you can say fish food.

What kind of small pets are we talking about? Lizards, frogs, snakes, mice and the like could all be captured and killed by a Flytrap or damage/kill a Flytrap during their struggles. In addition, as Tommyr mentioned, they require full sun, so placing them in a terrarium with your pets would not be conducive to the light levels these plants need.

You can certainly place several different types of carnivorous plants together, but keep the temperate species with other temperates and tropicals with tropicals, that way you can give them similar conditions year round as they need. If you plan to place Flytraps with anything, plant Drosera rotundifolia, Drosera intermedia, and Sarracenias together with them and use different levels of terrain, placing the Sarracenias lower so they are closer to the water level in the trays. Venus Flytraps and Drosera tend to prefer slightly higher elevations where they are not waterlogged. You can do that in a large pot or window planter. You do not need a terrarium at all, actually terrariums would be worse due to the chance of mold and bacterial infection, not to mention the inability to get good sun to the plants conveniently.

Venus Flytraps are native to North Carolina. You should grow them outside year round unless it gets below 20 degrees. Otherwisae a very thick mulching shoud give you enough protection. Down here in GA I grow mine outdoors year round. ~Terrariums Kill Flytraps~

i never said i was putting it where my pets are. i mean watering the plant with fish tank water