Hello @boubcher
Your second question is where you are correct that accuracy can be lost. If I convert from UTM to Lat/Long then there is going to be an "error".
In other words, the two systems are absolutely accurate in themselves, but when you convert between them, then you lose accuracy.
How much accuracy? Well luckily I covered this as a recent "question of the week" here: https://knowledge.safe.com/questions/100747/question-of-the-week-18102019.html
The best solution is to capture your data in one coordinate system, and keep it there. Every time you reproject you will lose accuracy. It might be a tiny amount, it might be a large amount. It depends on the coordinate systems you are converting between.
The only time I see one system being more accurate is where the coordinates drift over time. Then a new coordinate system might be created that is more accurate (for example GDA94 superseded by GDA2020)
I hope this helps to clarify.