1. What are your thoughts on what is said about the Jews at the start of the chapter? Where do you think they fit into Modern Day Christianity?
I believe that they were once God's chosen race. However I believe that isn't the case any more. See, I believe that the laws of the Old Testament, the need for sacrifices and such was Plan A for redemption with God, and that the New Testament, Jesus' crucifixion, is Plan B. Plan A required the Jews to be God's chosen nation, but Plan B puts everyone on an equal playing field, not requiring them to be of Israel. In modern day Christianity I see Jews the same as everyone else. Every has sinned, but through grace, all have the chance of being made right with God. Being of his chosen nation doesn't make them any more or less deserving of it, seeing as nobody is deserving of it in the first place. It is by God's grace that we get that chance anyway.
2. Paul describes people excusing their evil by saying the contrast makes God look greater. Do you think this is a fair justification? Why? Why not?
Saying their sins are used to contrast how great God is is a human excuse. God and sin cannot coexist, therefore it is impossible, and in my eyes to compare God to sin even with the reason being to contrast them. You can justify it all you want. But in the end Sin is Sin, and Evil is Evil. Though God doesn't expect us to live perfect sin-free lives (as that is impossible) I believe he expects us to make the attempt, and to accept that we have done the wrong thing when we sin, not try to justify it, especially in His name.
3. Do you find the Old Testament Law to still be relevant after the crucifixion and resurrection? Why? Why not?
This is a tough one. In some scenarios, I dislike the old testament, as people who try to fight against what the Bible says use it out of context. When I do see ancient laws used out of context, I tend to refer to this:
Spoiler:

Matthew 22:36-40New Living Translation (NLT)

36 “Teacher, which is the most important commandment in the law of Moses?”

37 Jesus replied, “‘You must love the Lord your God with all your heart, all your soul, and all your mind.’ 38 This is the first and greatest commandment. 39 A second is equally important: ‘Love your neighbor as yourself.’ 40 The entire law and all the demands of the prophets are based on these two commandments.”

In my eyes, Jesus has basically said that all other laws are insignificant compared to those about loving God and loving others. In my eyes the old laws that aren't about what Jesus decribes in those verses are gone. So it is still wrong to steal, lie, cheat etc like in the Old Testament, but it isn't wrong to wear clothes from two different types of material like in the Old Testament.

Did any verses stand out to you?
27 Can we boast, then, that we have done anything to be accepted by God? No, because our acquittal is not based on obeying the law. It is based on faith. 28 So we are made right with God through faith and not by obeying the law.

Did this chapter raise any questions for you?
I struggled to understand what the court analogy/statement meant, but other than that it was pretty clear to me!

I agree with what you are saying about Jesus in the modern day Neo. I mean back when he was on earth, for people to hear him, they would walk a long way, and follow him around, standing in small confined spaces just to hear him speak. But now, when a new iPhone is revealed, thousands of people can watch it as it happens, from their own homes, hell, they don't even need to get out of bed. Back then, if someone had an opinion, it would only travel as far as it is spoken. Now, if I have an opinion, all I need to do is post it on Facebook or PXR for hundreds to see it. A few seconds of typing as opposed to going around and telling everyone. That can be used for both good and evil.