How mushy is the stem. Is it just soft or mushy. If it feels mushy, you probably have stem rot. You should be able to save the top of the plant and start over. I will let someone else better acquainted with this plant to tell you about propagating a new one.

I will talk about the roots. The roots should be white and firm. If the are brown and mushy they are rotted.

It sounds like possibly, when you have potted this plant you never removed the older soil from the root mass. This is a different type of soil than what you used, so it will hold a different amount of water and for a different amount of time. You always want to plant using one type of soil for the whole thing. This means removing the old soil, by washing it off with the kitchen sprayer or slowly removing it with a soft paint brush.

I let someone better acquainted with your type of pest to answer that part of the question as well.

Why is it tall and lanky? That is because it is stretching to reach the sunlight. It is not getting enough sunlight for the amount of water it is getting. In winter you want to cut back on the watering. Only watering when the soil it completely dry. Use a bamboo barbecue skewer to determine if the soil is dry. If the skewer comes out of the soil dry after 30mins, then it is time to give your plant water.

I am a big believer in using artificial lighting in winter. I believe a bright window and a cheap LED grow light will help keep your plant from getting too lanky in winter. A lower power grow light for 12-14 hours in the winter. In the summer it should have 16-18 if it can not get enough sunlight from a window or outdoors. Some of my plants are on grow lights year round, because I have more plants than I have space outside to put them in summer. So, I need to give them grow lights even in the summer. I use higher power lights, but cheap lights work great for supplemental lighting with a window.

In the winter a south facing window with the light. I live in Canada, I know what is like not to get much light in winter.

It's a lobelia relation that grows on vertical cliffs in full light in nature = needs good drainage and strong illumination, probably really wants to be in a bright, humid, well ventilated greenhouse. Like one might grow orchids in. (And is not of course a palm or even palm-like).