If I need to go away for a while, then should I turn off cable/wifi, or to leave Tails connected? First option looks better because physically disconnected, but multiple connect-disconnect can cause some additional edge effects and risks? (sorry if stupid question)
It doesn't matter. If you turn it off you save electricity. If you leave it on you don't. Neither will necessarily affect your anonymity.
What's best is to understand exactly how Tor works.