They pee a lot, don't they!
I know what you mean.
On the lapping of food - that'll just come naturally. So you'll have to let her figure it out.
On the litter box - with ours, we discovered some poo on the floor one day and was like, "She's going poo on her own!!" So that's how we knew she was ready to for some litter box training.
We got a kitten-sized litter box and put her in there (with litter) and raked her front paw through the litter to show her how to dig in it. We put her poos in there, and whenever she peed, we put that in there, too. We would either stimulate her over the box or put the pee-soaked paper towels in there.
Honestly, once she started going on her own, she hated being stimulated. She would make an even bigger fuss over it than normal.
So yah, that's what I would try. If you don't want to invest in a kitten-sized litter box (which she'll outgrow), you can always get the disposable ones that are made out of cardboard. You can cut down the sides for her (so it's easy for her to get over the sides with her short legs).