is my fast broken in these two cases?

1. i put lip balm on after isha and when i woke up for suhoor i wiped it off with tissue and rinsed it off with water so did i wipe the lip balm off correctly? or because i thought i did and swallowed the fast is void? 2. i made wudhu 2 mins before fajr and i put the water more back in my nose and my mouth because i heard to put it farther back if fasting hadn’t started so when i started to pray fajr i swallowed and was doubting whether or not i swallowed water is my fast valid?