It sounds like she has a serious respiratory infection .... she may be opening her mouth like that because she is gasping to breath
If so, she needs to go to a vet experienced & knowledgeable in treating rats asap
You can give her a tiny piece of dark chocolate to try to keep her airway open
You can take her into a steamy bathroom to see if it helps ... But if she struggles or seems to get any worse have more difficulty breathing etc Get her out of there Immediately as she has fluid in her lungs and the steam will make it impossible for her to breath.
She likely needs to be put on antibiotics immediately. Likely baytril + azithromycin (10 mg/Ib) orally, twice a day for at least 6 weeks.
The azithromycin comes from a drug store by prescription from the vet.
(It takes a few days for antibiotics to start to make a difference so she needs to start asap)
She will also need Lasix if she has fluid in her lungs.
Otherwise she may need to be humanely put to sleep by a vet who knows how to do it properly (most don't)
see
http://www.ratshackforum.com/forum/showthread.php?t=7652
She is likely losing weight because she can not eat and try to breath at the same time.
You can a post a video of her breathing ..........
But from what you have written it sounds like she is in respiratory distress
and needs help asap
If she has lost that much weight then she has been ill for awhile and will probably not survive much longer
She may also be dehydrated
and there are things you can give like organic soy infant formula thickened with a bit of baby cereal, her blocks made into mush, peas ...
But it sounds like she needs a vet and meds immediately