Impurities

Will an object be impure if there are no signs of impurity visible?

Q:

1. If someone gets scratched by a persons nail accidently and blood begins to flow or a person gets cut with a knife and blood begins to flow but no blood can apparently be seen by the naked eye on the person (who scratched you) nail nor can blood be apparently seen by the naked eye on the knife, does the person who scratched you have to wash his nail or does the knife become napaak and have to be washed even though you can apparently see no blood with your naked eye?

2. In a similar scenario, if you are not sure when or which object cut you and caused blood to flow and no blood can apparently be seen on anything or a glass shatters and a piece cuts you but you are not sure which tiny piece that is now scattered on the floor cut you and no blood can apparently be seen on any of the pieces, do you regard everything in the vicinity as napaak even though no blood can apparently be seen by you on anything?

Vomiting several times in small amounts

Q: I have read in Bahashti Zewar that vomit that does not equal a mouthful is not regarded as impure in Shariah but if a person vomits small quantities several times and these small quantities together equal a mouthful then it will be regarded as impure. I have also read on the internet (I'm not sure how reliable the following information is) that if a person vomits small quantities several times for the SAME REASON then if together it equals a mouthful, it will be regarded as impure.

1. My question is that if a child vomits up a small quantity of milk while burping after feeding and this happens every time after feeding that a little milk is brought up while burping the child (as usually occurs with babies) then will it be regarded as impure as this is happening for the same reason (burping) and after a very lengthy period, if a person had to add up all these tiny amounts it will eventually add up to a mouthful?

2. Will the same ruling apply to an adult who sometimes when burping after eating, a tiny amount of food is brought up or a small amount of bitter saliva that doesn't equal a mouthful but if after a couple of days it is added up, it will equal a mouthful?

Impurities on one's shoes

Q: Please can you help me with the following?

1. I was walking outside and there was an area which had a lot of stool from various birds, I tried my best to avoid it but am not certain if I avoided it completely, does this make the bottom of my shoes napaak?

2. If a non Muslim is eating a sandwich and I am not sure what the content of the sandwich is (i.e. if it contained something haram) and they subsequently touched me on my back, does this make my clothes and the seat my back subsequently leaned against napaak?

Is mucus or phlegm impure?

Q: Are any of the following regarded as impure in Shari'ah?

1. The mucus or phlegm that comes out of the nose or throat due to a cold, flu or sinus infection

2. The yellowish white mucus or phlegm that comes out of the nose or throat due to a cold, flu or sinus infection

3. The yellow or green colour mucus or phlegm that comes out of the nose or throat due to a cold, flu or sinus infection (could be pus).