I like the sound of what your planning!
For the first question, I think you should use LiPo batteries, but have them take up the same amount of space as the cylindrical cells would have. the longer you can play the portable for the better in my opinion. Also, the size of the portable would be comfortable to hold if it's the thickness of an N64 + cartridge. you don't want to make it so thin that it's uncomfortable, but then again you don't want to make it uncomfortably big either.
For the second question, having the memcard/rumble slot stick out the back would be better weighted when using the rumble or transfer pak, and also the rumble would feel more real with it sticking out the back. But personally I don't think it would look as good as having it slot upwards from the bottom.. ..so I guess if your going for the best functionality you should have it sticking out the back, but if your wanting these things to look the best the can stick it on the bottom.
It's also worth keeping in mind how often you use each accessory. like.. transfer pack = pokemon stadium.. rumble pack = never.. memory card = holy magic century. that's my experience of using the controller accessories. I think there are more games you would use the memory card for than the rumble or transfer paks. So it might be worth going with aesthetics and putting the memory card on the bottom sliding up. and then if you ever NEED the rumble or transfer pak they still work.
Those are my thoughts on this, hope they help lol
