your alocasia is an aroid, not a palm. try the aroid forum. It is a type of elephant ear. see, your learning already!

The alocasia should be watered whenever the surface of the soil starts to feel dry, you can use your finger to test. Water enough so that the extra comes out through the holes in the bottom of the pot, but don't let that water sit there. They will grow better and more quickly with more sun than you can provide indoors so I don't know how long the plant will look decent inside.

The dripping water is a normal thing in Alocasias, I see that with mine when I start growing them indoors in the spring. It happens with banana plants too. It is definitely not because of lack of water.

Use a knife to slice off the lower dying foliage close to the stem, or wait for it to get very dry and just pull it off.

To make it thrive indoors, place it next to a large east or west window, give it a larger pot with good soil, and use a general purpose slow-release fertilizer with supplemental liquid feed during the warm months.

Read more info about growing plants indoors, lighting, soils, diseases, etc. on the internet, and don't be upset if things don't grow as well as you think because that is what will inevitably happen to beginners; but that will encourage you to try again and improve upon your previous failures.

My persian palm came w/2 suckers on it, I separated them about 8 months ago, it has not made any new ones yet, but it has a new sprout that does not look at all like a leaf. Are these plants capable of flowering ?