1. Is it okay to play with temporarily soft hands (after doing dishes/taking bath)?

2. Should I peel the dead flaps of skin?

3. Why the hell aren't my finger tips nice and smooth to begin with?? I know the strings are tough on your fingers but I've been playing for a while now and I've always had nasty chewed up fingertips (when I look at other guitarists, they have smooth callused fingers). I'd suspect maybe diet..
When you play, callous builds up, and essentially callous is dead tissue. It's normal for it to tend to flake off and peel and everything else.
If you have rather oily skin like me, this isn't much of a problem. I have typical thick callouses (I'm an acoustic picker) but they don't tend to flake much.
However, if you have dry skin and/or you are in water/detergents a lot... May make the problem worse.
Try wearing rubber gloves when you do such work, and consider some sort of mild lotion or moisturizer... Shouldn't affect the callouses but may keep them from being so flakey.
just steal your sister's emory board and file it off. i get a strip of emory cloth when i visit 'ye locale car mechanic. he has rolls of it...more manly than your friends catching you with the butterfly covered board your sister has on her dresser.
i used to use VERY fine sandpaper or the finest emery board and VERY lightly sand the tips of my fingers so they wouldn't develop into loose flaps of skin. if you peel off the flaps, you can cause bleeding and possibly infection, and will have to start your calluses from scratch.

btw, when i used to play a LOT, my calluses were always flaking off. i don't know why, but no matter what i did, i never developed thick callus. i was jealous of my husband, whose calluses never flake, are thick and stay thick.
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You can just moisturize them and it prevents them from flaking off. I don't have mega callouses, but I do have noticeable ones that don't crust up as often as they used to. Filing or sanding it off doesn't fix the cause which is dryness. All it really does is make them neater to look at, but they'll get bad again later.
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I recommend that you don't play when your fingertips have been softened by washing dishes or taking a bath... play when they are nice and dry, or the strings will tend to cut into your fingers more than necessary.

In my experience it takes about 2 years of playing, an hour a day, to build up good caluses.

The caluses are not like smooth pads... they have a noticable groove in them, which is where the strings most often tend to go.

Don't bite or pick the caluses... just leave them alone.

I use a moisturizer after bathing (Cera Vea) and naturally I get it on the fingertips as I am applying it, so perhaps that's why I have never noticed much flaking off of dead skin... and I'm naturally dry skinned (I also live in Arizona, where it's rather low humidity most of the year).

One other thing... if my finger start to hurt after playing for a while, I think it's wise to stop, and prevent them from getting really sore. By then I'm usually tired of playing, anyway.

Oh yeah... use the lightest strings that work for you... no sense making life any more difficult than it has to be !

Good luck,