There's nothing wrong with washing cast iron with soap and water and it does not hurt it to let it air dry, assuming it's set in a rack so air can circulate freely around it. I've also always stored mine with the lids on and never had a problem, but those who live in a more humid climate might have problems with rust.
I also let mine soak, sometimes even overnight if I'm extra lazy, with no harm done. I avoid that if I've made chili or some other tomato-based dish in it though. Cast iron generally is easier to wash when it's still warm, but not so hot you can't easily and safely handle it.
The worst thing for the seasoning is steaming. Since I've started cooking healthier and using more water instead of grease for cooking, I've had a harder time keeping mine seasoned.
Cast iron is brittle and can warp or crack if subjected to extreme temps. So for example, it would not be a good idea to store your cast iron in the unheated garage in Minnesota in January, then bring it in the house and throw it on a hot burner without letting it come to room temp first. Similarly, it's not a good idea to take a hot CI piece off the stove and run cold water in it. Either move could ruin it.
If you need to strip all the old seasoning off, simply run the cast iron through the self-clean cycle in your stove. This also works for stainless steel and cast aluminum. I particularly like using that method for grungy grill grates from the barbecue grill. Don't use it on anything that has plastic or wooden parts or non-stick coatings, etc. Do it at your own risk though with anything other than cast iron. I've never had any problems in the many times I've used that method, but like most things in life, there are no guarantees.
If you need to remove lots of rust, use electrolysis. Works great and it's effortless.
To season cast iron, first remove all the old seasoning, rust, etc, down to the bare metal. You will need to re-season immediately or the piece will start to rust. Rub or brush on the thinnest layer of cooking oil, Crisco, mineral oil, or Camp Chef Cast Iron Conditioner possible, making sure you get every bit covered. Set the pan upside down in the oven. You may want to put some foil under the pan because it may drip as it bakes. You can place more than one piece in the oven. I usually jam in as much as I possibly can. Bake for one hour or so at 400 degrees. This can get smoky, so turn on the fan over the stove and/or open up the windows. You may have to disconnect the smoke alarms. Usually one piece isn't too bad, but if you have a whole oven full, it's going to get smoky. If smoke is still coming out of the stove, then your iron is not seasoned yet. Basically what you're doing is burning the oil onto the pan and creating a carbon coating. Once the oil has burned to carbon, it will stop smoking. Turn the oven off, leave the door closed, and let the whole works cool overnight.
In the morning when you pull your newly seasoned piece out, it may look brownish instead of having the deep black patina you want. That's okay. It's fine to use as is, or you can slap on another coat of oil and go through the process again. In
this picture, you can see the top pot has a nice black patina, while the brand-new DO under it looks brown because it has only one coat of seasoning on it. Either surface will work equally well.