Factors that break and don't break the fast

Scarf coming in one's mouth while fasting

Q: Frequently, when going in sajdah, the fabric of my headscarf or the prayer mat ends up on my lips or in my mouth. This is an issue when I’m fasting. I don’t know if anything like microfibers or small hairs have entered my mouth. Today this happened during salah but I couldn’t feel anything in my mouth after it occurred so I assumed I could swallow as usual.

1. Was this correct?

2. If this happens during salah, and I feel something in my mouth after, do I have to spit?

3. If this happens in salah or near the end of it, do I have to check in a mirror afterwards to see if anything inside my mouth?

Swallowing the moisture on one's lips after wudhu while fasting

Q: The moisture left on my lips from washing my face/mouth during wudu, is this safe to be licked and ingested when fasting? Usually after I wiped my lips in wudu, I have to spit and then let my lips air dry and/or wipe with a tissue until dry. Today after wudu, the majority of my lips were dry but in the corner of my lips I felt a coolness, which may indicate that there is still moisture from wudu left. I licked that area. So now I’m just wondering if my fast is valid. 

Mistakenly drinking water while fasting

Q: A person forgetfully drinks water in Ramadan. While drinking water he suddenly remembers that he is fasting. He stops drinking water but while he was remembering that he is fasting he might have drank a little water. That means he drinks a little water remembering that he is fasting, but he did not have any intention to break the fast. He then continues the rest of the day fasting. Is his fasting valid?