Re: Crib in the bathtub?
A pack n play would probably fit well in a tub.
You wouldn't be looking at the baby being able to climb out for a long time, maybe a year or more, unless your baby is a monkey (some are!) so I wouldn't worry about that at all. By then, your DD1 might be outgrowing her need for so much dark and quiet and baby would be ready to room share.
One thing to remember is that just because your DD1 is a huge sleeper, doesn't mean the next one will be. My youngest, at 11 months, barely sleeps 9 hours at night snd has one 45-minute nap a day. Her three older siblings all slept 11-13 hours at night and took 2-3 naps a day that were 1-2 hours each. Her sleep patterns are so different!
Close the lid when you flush, then no risk of "fecal matter flying up into the air". Multiple studies have shown there is no more fecal matter on a toothbrush stored on the back of a toilet than a toothbrush stored in a closed closet. It is everywhere.