Kitten using potty and staying & hiding in litter box

Kitten 14 weeks. I recently got a covered litter box because I thought it would look nicer and because my kitty had just started reaching back in the litter box and scooping a pawful of litter onto the small run I have under it. It is just a little litter and from the corner. When I caught her doing it, I distracted her with a toy. Anyway, I thought that with the covered litter box she wouldn't be able to do this. Well, she is still reaching back in, but not able to pull the litter out. She is also sitting in there and hiding. When I see her doing this, I shake one of her toys to get her attention and she comes running. Why is she all of a sudden doing this? I scoop every day and then change the litter once or twice a week. I'm home with her and play with her a lot. The only thing I did different was to stop using liners and that was a week ago. This just started in the last couple of days. She took to the covered box right away, but just in case I haven't removed her old box yet. She adjusted to not have liners--she clawed up the old one and pulled all the sides in when she covered up.
One more question--I have just had her for 7 weeks and have her food and litter box in the laundry room. Do I at some time need to move her food? They are about 6 ft apart. Thanks for all your help.

It maybe she just likes the privacy in her new covered box. Cats like to be surrounded in things(My cats LOVE boxes) and if this is the only sort of hidaway she has she may just like the security it provides. Then again I'm not sure if you already have something like a kitty tent for her to hide in. It doesn't sound like there's anything wrong if she comes out to you when you call her.
As far as her food placement goes if she doesn't seem to mind where you have it then I'd leave it. Or if you have a better spot then slowly move it to that spot a little bit every day.

Like BadHabit said, cats love privacy, especially in boxes! (or covered litter boxes for that matter!) My cats will always hop in and hang out in a box if there's one around. And my cats also like sleeping under my bed, under the fish tank stand, and under couches, chairs, anything really. It sounds like you've got a normal healthy kitten on your hands!

Thanks for the replies--I guess I'm a little concerned that if she's hanging out in the litter box, isn't that a little germy? I do have a small box in the family room that I put her toys in--I'll just take the toys out and let her play in that. Thanks again.