Turning appliances on and off: This is why I caution people against the word “using”, in favor of “operating”. Using them is okay, as long as we don’t operate them, i.e., turn them on or off or adjust them in other ways.
Heat and a/c: We set them before the Sabbath. If one forgot or the weather is unexpected, it often becomes a big enough health issue to warrant asking a non-Jew’s help. Especially in winter.
Refrigerator: You hit the nail on the head. Just leave it plugged in, and you’re not operating the cooling elements. But the light is indeed a problem. We unscrew ours; some people put tape on the switch. If one forgot, it will depend on what foods are available outside of the fridge. If one can manage without the stuff inside, great. But if declaring the fridge to be off-limits will make a severe enough impact to ruin one’s enjoyment of the day, it will probably be grounds for asking a non-Jew’s help. This is an example of an area which is easily abused or misunderstood. If one lives alone and was only planning on a peanut butter sandwich anyway, he is not justified in asking a non-Jew to get the cold soda from the refrigerator. But if he has a whole family and guests, and the appetizer, main course, and side dishes are all trapped inside, that’s another story.
Bathing: There’s lot of details, but basically you nailed it perfect.
Shoelaces and ties: Sorry, Chronos, good guess but wrong. The distinction goes by the permanence of the knot. Two factors are critical: The intention for the knot to be temporary (i.e., one plans to undo it within 24 hours), and the style of the knot to be temporary (i.e., one does not need to pick the the strings, but simply by pulling at the right place the whole thing will fall apart).
The shoelace knots often in use (where two loops are joined by a simple knot) are a good example of this. If one pulls on either end of the lace, the whole thing becomes loose. Some people add an additional loop for security, and that pushes the whole thing into no-no territory.
Similarly, there are different styles of necktie knots. The one I use, if I reach under my collar and pull the narrow part of the tie up and out through the knot, the knot falls apart, and that is okay. With other necktie knots, if one does that he is left with a knot in the tie. That’s no good. People who don’t have the knack for my kind of knot will tie the tie on Friday afternoon, and then on Friday night they’ll loosen it off their head without untying it, so that they can easily put it back on Saturday morning.
Elastic bands on a pony tail: No problem. Rubber bands of all sorts (and their even more modern cousins, the metal keep-tie) are great solutions for many Sabbath situations.