Basements inherently have more humidity. To combat this, have your entire concrete walls and floors sealed with oil based watertite. Otherwise you will need the dehumidifier to run all the time. It is possible your airflow is not sufficient, causing the ductwork to get very cold which will increase condensate. So possibly increase ductwork and insulate the ductwork with a vapor barrier are more solutions to try. I would not try to use the AC to dehumidify the basement, basements typically are cold enough and if you run the AC in the basement they get uncomfortably cold.

No issues at all with the T1 heat pump, nothing is exhausted to the air. There is very very little heat that is pumped out during a cycle which comes out the bottom of the dryer (if you have it stacked and have the drawer you will notice the contents of the drawer are slightly warm). From a lint perspective, when you scrape the two lint filters after a cycle some may go airborne (as with any dryer) but it's very little. I think you might have seen a Miele vented dryer that was vented inside into an 'indoor dryer vent trap'. These you have to fill with water to try to trap some lint from the exhaust and there will be lint all over your walls if you don't keep up with it.

It would probably be a good idea to call repair service and then have him explain it all to you, and watch carefully, so maybe it would be something you could do, if it happened again. Water running on to electric is not a good idea, so I would call repair service, sooner rather than later. It is unfortunate when things happen when you are all excited and just moving in, but, it does sometimes. First night in one of my homes, I woke up to go to the bathroom, and stepped in water. The hot water heater had sprung a leak. After turning off the water, my hubby and I spent the rest of the night with a wet vac, cleaning up the mess.

"In winter, when the furnace is running we get heavy condensation on the ceiling due to the heat hitting the cold ceiling." Warm air contacting the uninsulated ceiling surface may or may not result in condensation forming on the surface. Condensation occurs when the temperature of the surface is at or below the dewpoint temperature of the air. While the condensation could be the result of a leak in the furnace exhaust, it's more likely that the the furnace is heating the space surrounding it and evaporating moisture that is in the surrounding basement walls. It's not clear without more information whether the space needs to be insulated or whether moisture control alone would be more appropriate. If it's not a leak in the furnace exhaust, I suggest you consult with an insulation contractor who understands building science principles.