"If they are not Christian, how would they know they need saving? Does God let everyone know this personally, or do they have to hear it from another person or book?"
There's always a lot of close-cut defining and even sharp controversy about what is meant by "being saved," but my own thought is that at some point --- maybe it takes a stage of maturity, some hard life experience --- that makes people realize...
"Something just ain't right."
You realize it about yourself: "I do bad stuff that I said I'd never do." ... "The human race seems tawdry, corrupt, ignoble." ... "But I'm human too, and I can't claim to be above or aloof from that sort of thing." ... "Where am I going? Nowhere, it seems." .. "What am I here for? Nothing, it seems." ... "Life is a tale told by an idiot, full of sound fury, signifying noting." (Shakespeare)"
At that point, you've got an inkling that, "No, I'm not OK."
You realize that you were not just born into a life that's free and easy and satisfying in all its natural aspects. Actually, you were born into a predicament. Something is really uncomfortable, around you and IN you. And you can't really make it all "OK" on our own. And that's the beginning of wisdom.
"If God sorts things out for people of non-Christian faiths, what is the wrong with not being a Christian?"
One must not presume upon God, that all you need to do is coast along and He'll sort everything out. If that were the case, the Bible would not be full of imperative verbs like "Turn from your evil deeds." "Listen." "Choose life." "Repent and be baptized, every one of you." (Acts 2:38). And many other messages in a commanding tone: yes, this is imperative.
The fact is, every one of us in the human race is in a desperate position, as described above. If you just "go with the flow," you're going right over Niagara Falls to death --- an absurd death, and limitless personal destruction.
You come to realize this. You say, with St. Paul, "What a wretched man I am! Who will rescue me from this body that is subject to death?" (Romans 7:24)
God has provided for salvation through Jesus Christ, who is both God and Man, the only possible way to be rescued from corruption in every dimension of the word: moral corruption and the loss of your mind, death and rotting away. The only way to be safe is to be united with Him. I mean that literally: to become part of Him. To be incorporated in Him. To be joined to him, like a branch is joined to a Vine. He is Life. You need to be connected to Him as closely as ever you can.
"When a non-Christian prays and asks to be taught His way or needs help, does God hear them?"
((((Big grin))))) --- ABSOLUTELY. God is delighted to receive such prayers, at any time, from anyone. Anyone who approaches with sincerity of heart. He will supply everything.
Even if you think to yourself, "Can I even say I'm 'sincere'? I'm kind of a weaselly guy. Half the time I think I'm bullsh*tting myself. Maybe I'm just flattering myself with the thought that I'm 'seeking the truth'."
Even if that's so, OK, you can pray for sincerity. You can pray for God to show you how to pray because you don't know how to pray. You can pray that God will accept you even though you know you're somewhat of a phony. (Not that I'm accusing you or insulting you here. When you're honest with yourself these things come to mind.)
No matter. "Ask and it will be given unto you; seek and you will find; knock and the door will be opened unto you."
That's a promise.
In response to your first para, I don’t think hard lives are just for Christians.
I don’t understand the rest.