Eternal life apparently, is available to only those who have faith, which makes this a conditional agreement.
Yes, it is a conditional agreement. But God asks about the least thing He could ask of us. Confess Jesus Christ as Lord, and believe in your heart that God raised him from the dead (Rom 10:9-10). Once a person does that, he is sealed with the gift of the holy spirit, the guarantee of salvation (Eph 1:13-14).
God agrees to give eternal life to those who have faith, or believe.
The question is:
What does it mean to believe in Jesus? Is it just a prayer? Is it belief in the story of the crucifiction?
Rom 10:
9) That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
10) For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
To confess Jesus as Lord basically means that you make him "boss".
Is it living your life according to Jesus' teachings?
While Jesus is our example, living your life according to Jesus' teachings is not what saves you. Faith in him is what saves you (Eph 2:8-9).
Are we all meant to believe?
1 Tim 2:
4)
Who will have all men to be saved, and to come unto the knowledge of the truth.
2 Pet 3:
9) The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward,
not willing that any should perish, but that all should come to repentance.
Eze 33:
11) Say unto them,
As I live, saith the Lord GOD,
I have no pleasure in the death of the wicked; but that the wicked turn from his way and live: turn ye, turn ye from your evil ways; for why will ye die, O house of Israel?
God wants all people to believe, but He cannot force us. He gave us free will.
Does God know who will believe and who won't?
I don't think so. Others disagree.
Does God facilitate believe in some and not in others?
No. He want's all people to believe, and become saved.