I recently acquired a large banana plant but it died very quickly (part 1 of the story here). Now, pups are growing crazy! Not sure if I should get rid of the dead plant's trunk, and not sure if I should only let 1 or 2 or 3 pups grow and get rid of the rest... Also, the fastest growing pup's leaves don't seem healthy (see photos). I haven't been watering it very much, could that be why?
I would suggest cutting the dead trunk to the ground, unless you think it was diseased, in which case you may want to remove it altogether. As for the damaged leaves, they appear to face a bright sunny window and what looks like a baseboard heater. It is probably damage from dry air caused by the heater combined with very bright light and heat from the window. I would suggest moving the banana plant at least a foot away from any heaters.
I've turned heating off completely a little while ago, but good point regarding daylight! Because the plant faces south west and does get a good amount of sunshine in the afternoon.
I think you said in the original post that the pot does not have drainage holes. That makes it very difficult to keep plants healthy. They need air exchange at the roots. If you can repot it or make holes in the pot somehow it will help a lot. Individual banana plants do not last for a long time. It is not really a tree, but a very large herb. The trunk like thing is a group of fused leaf stems. It may only last a season and then the new pups grow. The pups look good. And I agree the leaf damage looks like it was probably physical.