Question: Is a way to pen a text file, read a few lines, close it, re-open it and start reading from the line where you left off before? Or do you always have to start from the top?

Answer: 
I would just start from the top each time. This is the simplest and possibly not much slower. You can use a RandomAccessFile but you would have to wrap it with your own line reader (as well as place some check that the file hasn't changed in an incompatible manner)
I'm pretty sure every time you open a file, it starts you from the beginning.