It's definitely safe to wire through the lighter plug, and often convenient.
Disconnecting the battery won't harm anything--it's a necessary procedure for various vehicle maintenance and repair activities, after all--but is less desirable in as much as it resets the computer and undoes any fine-tuning it may have done to its internal settings based on the operation of your engine and transmission. If your dash radio is connected to the chassis battery, it would naturally also reset the time and presets and so forth. In an RV the dash radio might well be connected to the house battery, depending on the whim of the RV maker.
If your RV is connected to shore power while its sitting, or if you have solar to keep the house battery charged (assuming this is an RV), you might want to consider installing a Trik-L-Start. It's a sort of built-in maintainer for the chassis battery, powered by the converter or whatever charges the house battery.