Hi there! Calvinism is complex and you will have to study reformed theology as a whole, not just the doctrine of calvinism alone to have a real understanding of the theology. It's easier for me to just adress the points you make as wrong or right according to reformed theology.
it doesn't matter what you do because Jesus has you or something.
Your brother is refering to those who are elected by God by His grace. (Unconditional election) However, your brother says it doesn't matter what you do, you will be saved since you have been elected. Romans 8:30:
"And those He predestined, He also called; those He called, He also justified; those He justified, He also glorified." This verse tells us that from the moment God chooses us, it is as if we are glorified in His presence in heaven. There is nothing that can prevent a believer from one day being glorified because God has already purposed it in heaven. Once a person is justified, his salvation is guaranteed - he is as secure as if he is already glorified in heaven."
But if you understand the whole theology behind calvinism, it's clear that the bible teaches us that all those who come to faith will not be saved.
“As for what was sown on rocky ground, this is the one who hears the word and immediately receives it with joy, yet he has no root in himself, but endures for a while, and when tribulation or persecution arises on account of the word, immediately he falls away. As for what was sown among thorns, this is the one who hears the word, but the cares of the world and the deceitfulness of riches choke the word, and it proves unfruitful.” (Matthew 13:20–22)
So you can lose your faith. Only those elected by God will be brought to faith and persevere to salvation. Does this mean it doesn't matter what you do, you will be saved? No, those who are chosen by God will follow His will and commandments. 1 John 2:3-6.
“And by this we know that we have come to know him, if we keep his commandments. Whoever says ‘I know him’ but does not keep his commandments is a liar, and the truth is not in him, but whoever keeps his word, in him truly the love of God is perfected. By this we may know that we are in him: whoever says he abides in him ought to walk in the same way in which he walked.” (See also 1 John 3:4–10, 14; 4:20.)
All of these verses show us that all christians will not be saved, and only those elected by God are able to keep His commandments and are saved by His mercy and grace. But then isn't free will in conflict with predestination? This seems wrong to you, and it doesn't make sense to any of us because we cannot understand it.
But God is omnipotent. For God all things are possible, whe cannot understand His will or His ways. Predestination and election doesn't make any sense to us, because we are human and we cannot even begin to understand His plan for us. Trying to understand God is an impossibility for us.
People say calvinism turns God into a monster, and they say that it's seems wrong just like you do. But when studying the bible we see calvinism is biblical and the truth. God should not be seen in the way we think God should be, but we should see God in the way he is. Many denominations say calvinism is heresy, because they don't see God in the way calvinism does. But for that there is Romans 9:14-
What shall we say then? There is no injustice with God, is there? May it never be! For He says to Moses, "I WILL HAVE MERCY ON WHOM I HAVE MERCY, AND I WILL HAVE COMPASSION ON WHOM I HAVE COMPASSION." So then it does not depend on the man who wills or the man who runs, but on God who has mercy. For the Scripture says to Pharaoh, "FOR THIS VERY PURPOSE I RAISED YOU UP, TO DEMONSTRATE MY POWER IN YOU, AND THAT MY NAME MIGHT BE PROCLAIMED THROUGHOUT THE WHOLE EARTH." So then He has mercy on whom He desires, and He hardens whom He desires.