Is one who prays with an incomplete ablution considered an infidel, as if he did not pray or abandoned prayer? And does the same ruling apply to ritual bathing (ghusl) from major impurity?

Whoever deliberately omits one of the obligatory acts of ablution (wudu'), their prayer is invalid, and they incur a great sin. They must repent and make up the prayers they performed in this manner. As for whoever omits something that is not obligatory, there is no sin upon them. And whoever did so out of ignorance of the obligation of what they omitted, their prayer is invalid, and they incur sin for their negligence in learning. It is more prudent for them to make up those prayers.