I am strictly a braintanner, so I do not know much about chemical tans. However, what I can tell you (OP) about your third question is that if you take an extra step, you should be able to wash your hides no problem. Now, this is the method for braintanning. I don't see why it wouldn't work on a chemical tanned hide, though like I said, I am not 100% positive as perhaps the chemicals render this method ineffective, so don't hold me to my words. I hope it helps.
After the hide is fully tanned, you "smoke" the hide. This entails literally infusing smoke into the flesh-side of the hide. The method that I usually use for smoking small game should work fine for you.
First, you need to acquire 4 boards of plywood, about 4ftx4ft (I go to Home Depot). Next, get some small nails or push pins and a claw-head hammer. Next, dig a hole in your yard about 1.5-2 feet deep and about 1.5 feet in diameter (these measurements are not super necessary, just to give a guideline). Now, using the push pins on the edges of the hides, pin as many rabbit hides as you want to 1 side of 2 boards (seems odd, you will see though). You do not have to pin them in a stretched position or anything special. Just pin them flesh-side out to the boards. In the end, the boards will be standing upwards on an edge, so try to pin the fewer hides near the edge that will be on the ground. Do not overlap the hides. After that is done, start a small fire in the pit and let it burn down to coals. Throw either sawdust (doesn't have to be super fine or anything special) or punky-rotting wood on the coals to suffocate the fire and cause alot of smoke to be produced. I, personally, have best results with sawdust. Now set up the 2 boards with the hides on them so that they lean against eachother, forming a sort of wood tent over the smoking pit, the sides with the hides facing inwards. Putting stakes in the ground at the base of the boards can help support this. Finally, set the 2 additional right up against the sides or "openeings" of your wooden tent.
This should entrap the smoke created by the smoldering sawdust. It's okay if the smoke leaks out a little; your goal is not to completely trap the smoke in, not that that would be possible. You just want a sort of smoke-sauna or smoke-bath to form inside the enclosed area. You want the hides to absorb the smoke into the skin. Continue the smoking for about 45min-1 hour. The more you smoke the hides, the darker brown they will get. The time limit I imposed will be practical and also give you a nice light tan color. Much more appealing than the white. Stay by the smoking pit the hole time to make sure the fire the not start flaring back up and lighting the sawdust on fire, singing your hides. If the fire starts up, just throw some more sawdust on top.
Now that your hides are smokes, wash them a few times, stretching them in between each washing. If you smoked correctly, the hides will slowly require less and less stretching after washing until they just don't need to be stretched at all. This is what you are looking for and at this point you can go ahead and makes gloves or whatever out of these hides. It's a bit of work, but imagine doing it for a 8ftx3ft deer hide, hahaha. Once again, this is for brain/mayo/egg/etc. tanned hides, so I am not sure if it will work for yours, though it should. Feel free to ask any questions. Lots of info on Google and what not as well.
What happens when it gets wet and dries?
When you "break" a hide (AKA stretching), you do not actually break the "fibers". The fibers you commonly here about are collagen fibers. They are what makes skin so elastic. When a youngster pinches his skin and lets go, it immediately snaps back into place like rubber. When an elder does it, the skin slowly sinks back into place like putty. This action is due to collagen. When skin of any kind dries up, the collagen fibers layer and tighten up and the moisture gets drawn out, sucking the fibers into each other. Like how a ball of clay tightens up and becomes hard and solid when left to dry. When breaking a hide, you actually are stretching out these fibers while they are still moist and flexible on a molecular level. What your tanning solution does (at least for brains/oils/etc.) is lubricate the collagen fibers so they can move freely within their matrix. This free movement is what makes raw, green skin or tanned skin so flexible, pliable, supple.
When you stretch a hide until it is dry, you keep the fibers constantly in motion so that they do not dry still and shrink into each other. It lets the hide dry out and lets the tanning agent take effect. This is why most tanning agents can't simply be applied to a hide and make it supple. Also why stretching a hide without tanning agent will not work. The fibers have to be stretched first in order for the tanning agent to work after-the-fact. It's all kind of complicated and I am trying to explain it in as short a writing so it may be confusing the way I explained it. If you have a question about a specific part just shoot and I can answer more in-depth.