Regarding the Straight Gate. Is it possible that the merciful and omnipotent God will allow a person to want to believe and be saved; pray with the intent to believe and be saved, want to repent and be forgiven, ask for faith to believe and be saved, but still fail to find that gate?
In a word, No. Romans 10:13 says that everyone who calls on the name of the Lord will be saved. Matt. 7:7-8 promises that all who seek will find, all who ask will receive, and to all who knock the door will be opened. John 3:16 says that whoever believes in Him will not perish but have eternal life. In John 5:24 Jesus said, “Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life.”
On top of that, 2 Peter 3:9 says that God doesn’t want that any should perish but that all should come to repentance. And 1 Tim. 2:3-4 says God wants all men to be saved and come to a knowledge of the truth. These verses tell us everyone who sincerely asks for salvation will receive it.
It’s important to remember that being saved is not a matter of trying to be worthy. We’re saved because of what we believe, not because of how we behave (Ephes. 2:8-9). As long as we sincerely believe that we’re sinners and that the Lord’s death paid the full penalty for all our sins, then as soon ask we ask Him to save us, we’ve met His only requirement.
In John 6:29 Jesus told us all God requires of us is that we believe in the one He sent. That means we believe that Jesus came to Earth to die for our sins so we could live forever in heaven with Him.
In addition, the Bible is pretty clear that the most important thing to the Lord is what’s in our heart (1 Cor. 4:5). A person who does all the things you described has shown a purity of motive that will not be overlooked by the Lord. He will make certain no one who shows that kind of desire to be saved will be turned away.