I am sorry to read of this, it must be quite worrying.
How old is your sister? the rough danger depends much upon age, the younger the person, the faster they need medical treatment.
Make sure to bring the container of eye remover to the hospital with you, and also to tell them how much has been swallowed.
I will describe the general properties of the chemicals you listed for you.
Aqua, is just the name used in many products for water.
Cyclomethicone is a mixture of various cyclo-dimethylpolysiloxane sillicone oil typ compounds, and appears to show fairly low acute toxicity, is nonirritating to exposed skin, and slightly irritating to the eye on continued exposure, apparently causing only mild liver damage and slight weight loss in lab animals, and is excreted in the urine.
Hexadecane isn't something you would purposefully ingest, although, probably not highly toxic, lower weight hydrocarbons are more volatile and can cause lung damage, the higher the weight, the less likely to cause such damage, hexadecane or its isomers are reasonably high weight hydrocarbons.
Butylene glycol, is chemically, 1,3-butanediol, it is used in foods as a humectant, to keep foods moist, so it fairly unlikely to be dangerous. (1,4-butanediol has CNS depressant effects, similar to alcohol and GHB in action, but I don't believe the 1,3-diol has these)
Sodium Chloride is common table salt, although in very young children, they cannot handle too much salt, older children will be fine after ingesting a little more salt than they should usually.
Rosa Centifolia, is an extract of that species of rose, used for scenting products, roses are nontoxic.
Propylene glycol is also used in foods, similar in properties to butylene glycol.
Citric acid, and salts of citric acid, known as citrates, are very widely present in foods, especially in citrus fruits such as lemons, oranges and limes, it is the weak organic acid which gives them their sourness, it is harmless.
Polyaminopropyl biguanide could POSSIBLY act as a hypoglycaemic agent, lowering blood sugar, from what I have read on diabetic oral therapy using biguanides, keep on the lookout for low blood sugar just in case, in an emergency, if your sister passes out from hypoglycaemia, give sugary sweets or drinks to boost blood sugar fast, I don't mean to alarm you or anything, just for you to be on the lookout.
I have also read a few accounts of biguanide compounds causing lactic acidosis.
Polyaminopropyl biguanide is used in the sort of cosmetic preperations you mentioned, as a preservative, in VERY low concentrations, one reference says a contact lense cleaner contains 0.00005% polyaminopropyl biguanide, so there really isn't going to be very much of it in any preperation.
the only danger I could imagine really, from this one, is kiling off of the beneficial gut flora, in a similar way as sometimes happens with antibiotics when their use is needed. You might try giving yakult, live yoghurt, or similar beneficial bacteria preperations, I reccomend actimel myself, my fiancee has it, and it tastes pretty good.
EDTA is not harmful, it is a chelating agent, its actually used in the treatment of some heavy metal poisonings to bind the harmful metal ions.
Iodopropynyl Butylcarbamate can be a contact allergen in some cases, it is used as a preservative, broad spectrum biocide, again, reccomend live yoghurt to replenish gut flora.
CI 42090 is a blue dye, I believe, known as Erioglaucine, banned now, due to its being carcinogenic, fairly unpleasant, but I wouldn't think a single exposure such as this will lead to carcinogenic effects.
I wish you the best for your sister, one thing you can try, is milk thistle extract, it is available in capsules from health-food shops, and it is a very potent protector of the liver and will help ward off any damage to the liver caused by ingestion of the eye remover product.