The recommended cellaring temperature is between 12 and 14 degrees depending on your personal preference. Whichever temperature you choose, the key is to remember that the temperature must be constant.
You can take out your wines to drink, however you would need to put white wine into a fridge or an ice bucket to cool down to your required serving temperature. Your red wines would need to be left out to come to “European” room temperature for drinking.
Yes, humidity is important in ensuring that corks do not dry out and shrink. This would allow air enter the wine and cause the wine to oxidize. Another symptom of low humidity is corks breaking when being removed.
Wine cabinets create condensation water due to temperature difference. The condensation water forms on the back panel of the unit, and flows down to the bottom where it is collected in a dish. The compressor heats the water and redistributes it as warm vapour back into the wine cabinet when it operates. It is maintained by the "thermal pump".
It is normal and is necessary for the maintenance of humidity. Just keep your bottles away from the wall so you do not block the water flow.