I think you should do whatever makes you feel comfortable. Personally if I am actively using a Carto on and off
through the day or even over a couple of days I don't place any caps on them. The caps (never liked the term condom) are meant for storage before use so the filler doesn't dry out.
As for leaving the Cartos on the battery, I do, but some folks don't. I know that you should never leave the Cartos on p/t when not in use, as far as that goes you probably should not leave it plugged into the USB port when not in use.
Unless the battery is activated via drawing on it (auto) or pressing the button, simply leaving the Carto on it shouldn't draw down the battery. I have read 1 or 2 stories of Autos with a Carto attached heating up, but I think these may have been a different type noise activated battery.
I generally have 3
batteries ready to go at all times and I leave the Cartos on them throughout the day. Never had a problem.