Laptops tend to be energy efficient. Generally speaking the energy savings are not that great with it being turned off. You can check the power brick specifications. Take the watttage of the brick and multiply it by 8 (or however long you plan to keep it off during the night). Now divide that by 1000 and multiply by your electricity price (generally it's given out by kWh so if it's different where you live adjust the numbers accordingly). That's how much money you save per night

For example where I live from one of the providers the cost is 0.227 EUR/kWh (we could go down to 0.158 EUR/kWh if we use 2 timezone pricing since we only need the nighttime).

((60W × 8h) / 1000) × 0.227 EUR/kWh = 0.10896 EUR

So each day I turn off a 60W brick off for the night the maximum savings is ~11 cents or ~39 EUR per year. So that would answer your question of is it worth it. There is no real damage to the device for being plugged in 24/7. The battery may degrade, but at this stage battery capacity is irrelevant.

As for storage, external storage via USB is not going to be as fast, but in this case I doubt it will matter much, any peformance loss is likely to be negligable, though I can't be 100% certain. Try it out, worst case replace the internal drive later down the line if performance is an issue, though make sure that it's the I/O that is hampering performance and not let's say CPU or memory.