What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.
Is it obligatory for someone traveling by plane in the afternoon during Ramadan to fast?
Anyone who intends to travel after dawn must begin the day fasting and continue with the intention of completing their fast, as fasting was obligatory upon them before traveling.
However, if they experience unbearable hardship after starting their journey, they are permitted to break their fast due to that hardship, not merely because of travel. In such a case, they must make up for the missed fast later.
Should a prayer performer who forgets to offer the middle Tashahod (saying ash-hadu anala ilaha ila-alah) offer Sujood As-Sahw (prostration of forgetfulness)?
He/she should offer two prostrations of forgetfulness at the end of the prayer. And Allah Knows Best.
What is the ruling on someone who doesn`t perform prayer?
All perfect praise be to Allah,The Lord of The Worlds Not performing prayer is a major sin, and one who doesn`t pray out of laziness is considered an oft-sinner ;whereas, the one who denies that it is mandatory is considered a disbeliever. And Allah Knows Best.