I’m a new convert to Shia Islam recently, and I have a surface level understanding of rules regarding fasting (I did a decent amount of studying before I converted).

But, considering I converted this month, and we are already the majority of the way through the month of Ramadan, do you suggest that I fast, and if so, do you suggest that I follow all of the rules to my best ability, or would you say there is more leeway considering the circumstance?

Yes I highly encourage you to fast the remainder of this month, trying to follow the rules to the best of your ability. God doesn’t burden us more than we can bear. So to the best of your ability is sufficient.