The car is not like a cellphone...once it gets charged up, it disconnects the charging voltage. If you ask it to program a departure time, when that starts up, having it connected, it will likely turn back on so it doesn't drain the battery in the process. I've seen the departure time routine draw as much as 20A or so from my EVSE. If you're using a level 1 unit, the EVSE won't be able to keep up (but it won't hurt it). The battery warming heater can draw as much as 1Kw/hr, and the cabin heating/cooling maybe another 2-300W or so. My EVSE seems to draw about 3W when connected to the car and the car is not charging. That's likely the internal power supply in the EVSE and the interlock signals going between the EVSE and the i3 drawing that (small) power.
One report I read stated that charging 10x from 90% was the same wear on the battery as once from zero. I like to always leave with a full 'tank', and in over 3-years, have not seen any battery degradation issues. I almost always plug it in when I get home, even if I am going out later and would have enough charge to get me there and back.
