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You are very correct! This is a typical case of being over-watered. Now what you will have to do is let them dry out very well. Make sure to give them plenty of light from a window, and I would also recommend using wettable sulfur, or garlic oil in the soil, in case any root infections are setting in. Make sure to let the top layer of soil dry out between watering.

This plant has an interesting property... It has the ability to self regulate water! This is the plant's defense for overwatering. to stop the dripping, make sure that the soil stays slightly moist, but not saturated, and not dry. This will stop most of the dripping. Here is an article on their care: https://www.gardeningknowhow.com/houseplants/dumb-cane/growing-dumbcane-dieffenbachia.htm

There are a great number of things that could have went wrong here. These plants can be quite picky, although with some proper care and a great deal of time and effort they can adapt to many conditions.

This article will help you to figure out what went wrong: https://www.gardeningknowhow.com/houseplants/dumb-cane/growing-dumbcane-dieffenbachia.htm

If this white splotch is a web then this could be Spider mites. If it is just white powdery spots then it will be powdery mildew. The treatment will work for both, though. You can apply every few days, or as needed for tougher infections.

There are watering globes that stick into the pot, and release water slowly. These can be great for people that travel frequently, or even just an occasional trip. I believe this to be something to consider here.

This link will give you more information: http://www.goldensunlandscapingsvc.com/blog/how-to-use-watering-globes-for-plants/

60 should be okay as a minimum, not below.

https://www.thespruce.com/dumb-cane-dieffenbachia-definition-1902751