Definitely remove the dead babies. Is she still bleeding from the vagina? Can you put your fingers on her chest and check her heart rate? Is it slow? Are there any babies left alive? Is her abdomen rigid? Find your nearest vet. You said you live in the country? How far away is the nearest vet? One hour? Two? If the vet is longer than an hour away don't move the babies. If the mom is still bleeding from the vagina and has a decreased heart rate don't move her either. If you can, find a vet that does house calls. If not, I'm sorry but she won't survive if any of the answers to those questions are yes and you can't get a vet.
In the pics you posted the girl looks like a mouse from her tail and ears. Can you get us another pic showing its an actual pet rat?
yes remove the dead babies. Mom might be grieving but panting and porphyrin aren't good signs at all. Can you pick her up and look at her vagina, see if there's a lot of blood, or discharge? You'll need to smell it for infection as well. Can you hold her sides to your ear and listen to her breathing? Is it clear or is there crackles, wheezing, rasping? I would also clean that cage as the bedding looks very dirty and wet, which won't help and could cause serious problems. Put her on ripped up paper towel if you have nothing else.
Once you've done this we can talk about what she might need.
If you can get a vet on the phone and describe your situation they might have some pointers that could help too. If you have an eye-dropper you can try to give the rat some water or milk, she really needs to re-hydrate. One of the best foods for pregnant and nursing rats is hard boiled egg yolks so if you can get her to eat some that helps too.
Also, what kind of bedding is she on? Looks like cedar? If so, the shredded paper towels is wayyyy better! At the very least, clean her bedding out, and replace it with paper towels, and try to get her hydrated asap. I don't know if you've seen rat or mouse babies, but they look really deformed and alien like when first born. Make sure you aren't throwing away any live, normally formed babies. You can also give mom lots of soft foods, good for hydration. Cooked sweet potatoes, or leafy greens, or even some organic soy infant formula. But if she's lost a lot of blood, she may go into shock, and there's not a whole lot a person who's not a vet can do. She would need iv fluids immediately. Hopefully she pulls through. Also, after a particularly hard labor, she will be pretty exhausted. Please keep us updated on how she is.