Lori asked: How does one neatly fix mistakes?
Sadly, there are two answers your question. First, it depends on what mistakes you need to fix, and second, don’t make mistakes in the first place.
If the mistake is in a chain, and you are still in the process of that chain, just take a needle of some kind and carefully pick out the stitches. You are trying to loosen the thread so that you can put your shuttle back through in the opposite direction, and slowly and painstakingly undo the work.
If the mistake is in a ring, and you have not yet close the rain, same deal. If you have closed the ring, it is easier to give up, cut it out, and start over. It is sometimes possible to open a ring, but usually more pain than it is worth. I do not recommend even trying until you are very experienced and running out of thread.
I know this is not very inspiring, but I hope this helps a little.