is my fast broken in these two cases?

Question

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?

Answer 1

Note that for the cases you've mentioned the view of different schools of fiqh my deviate from what I found in fatwas.

Swallowing lip balm while fasting

The view of scholars such as ibn Baz, ibn 'Uthaymeen and ibn Jibreen here is that it is permissible to put creams on your skin or lipstick or lip balm and that it doesn't invalidate your fast nor your wudu'. However if this product has a taste and you swallowed it -while fasting- (and it reached the stomach). However here again it depends on whether you did so intentionally or out of forgetfulness:

"If somebody eats or drinks forgetfully then he should complete his fast, for what he has eaten or drunk, has been given to him by Allah."
(Sahih al-Bukhari and Sahih Muslim)

As a deviation I know about in the Maliki school of fiqh a safety measurement in case of forgetfulness is to make up this day at least.

See for example fatwa islamqa #92923.

Swallow or inhale water during wudu'

The matter mainly is similar if the water reaches the stomach it would invalidate the fast if it was done intentionally. And it would be a sin and one must make up that day (at least depending on the scholarly views).

Note that we are informed to:

Snuff up water freely unless you are fasting.
(Sunan abi Dawod, Sunan an-Nasa-i, Sunan ibn Majah and Jami' at-Tirmidhi)