Factors that break and don't break the fast

Doubts regarding one's fast breaking

Q: I'm making up my kaffarah fast (60 consecutively)

1. I was sweating, sweat dried and I licked my lips and swallowed it, did my fast break.

2. I have dry lips, my skin comes of, I licked my lips and the skin went into my mouth, I swallowed it, tried to remove it before doing so but couldn't feel it in my mouth, is my fast broken?

3. This is the second time I have started my kaffarah from scratch, my fasts keep breaking for stupid reasons like this, what can I do?

Surma while fasting

Q: Does it invalidate or nullify the fast if you apply surma and sleep during the day? My father has been arguing that while fasting if you sleep during the day with the surma, it nullifies the fast as per some mufti he heard. kindly guide me.