Tillandsia? Here is a link that might be useful:

If it is Tillandsia juncea, this one needs both regular watering plus good air circulation to be happy, compared to some other easier to grow Tillandsias such as T. bergeri under many California conditions. It is more mesic in its water needs, and I have killed this off if I let it get too dry, and also when it didn't get enough sun and remained too wet in winter. Otherwise it is easy to grow, and takes a bit of frost in winters. It will let you know if it is too dry by losing foliage and/or getting dry tips.

All I can tell from your photo is that it's a Vriesea. There are hundreds of species and hybrids, but the culture on the green-leafed ones is all about the same. Fairly low light-- not total shade, but better suited as an indoor plant near a sunny window than in full outdoor sun. Twice a week watering is probably plenty, and I imagine it likes the aquarium water. Broms generally benefit from having water in the center cup as well as the roots. Just make sure the potting mix drains well and it's not sitting in a saucer full of water. Your plant looks fairly healthy, and as long as it does I'm guessing that whatever you're doing is fine.

Opinions differ on when to remove the pups (offsets) if at all. If you can stand it, just leave them on til the mother plant is well and truly dead, removing brown dead leaves along the way then copmpletely remove the dead foliage. People who can't stand it, or growers who are trying to get several plants off of one mother before decline, will remove the offsets when they are about 1/3 the size of a mature plant...sometimes removal spurs the mother to produce even more offsets. But, depending on species, your plant may not work this way. Neoregelias will hang around for a long long time and decline more slowly, allowing many offsets to be removed sometimes, while I have found Billgergias tend to crump a little faster. Unless you just don;t like the pot your plant is in, you can leave it there. Many species of bromeliads can be pretty much 100% epiphytic, in the rainforest they grow in the canopy layer attached to trees, rocks, etc. Its actually pretty dry up in the canopy, which is why they have evolved as epiphytes, developing the specialized cells in the water holding tank/cup that allow them to be watered that way. But they can and still do take water and nutrients through the root systems. For many plants, the only reason they have roots is to anchor them to something or into the ground.