An answer to "How to widen the groove on the nut" :
1) Read the other answers here warning you about what happens if you get it wrong (Tim & Dr Mayhem). If you still want to proceed ..
2) Remove strings - maybe you can just remove the relevant one but it's probably best to give yourself a bit of room so better to remove them all.
3) put a bit of paper or cardboard up against the nut and on top of the frets, to protect it.
4) ideally add something to protect the neck beyond the nut
5) If possible, put something up against the nut, layed flat against the frets, which butts up agains tht enut at the level that the groov goes down to. This will stop you making the hole any lower, whcih you probably want to avoid.
6) Get either a small (model/jewellery making) file of the right size (ie, just a bit bigger than the existing hole) and GENTLY file the groove wider. Don't file it lower !! you'll make the string buzz as it'll sit too near the frets.
6a) Alternatively, you can use a bit of folded sandpaper - use very smooth, maybe 1200 grit ("wet & dry") so that you don't take off too much at a time.
Pull the file/sandpaper sideways across the nut - don't push down against the neck.
7) Repeatedly try the string in the hole. Try the string at full tension. Do this a bit before you've got the hole large enough because this will give you a clue how much you need to take off. If you're lucky, the string will leave a mark on the groove where it's meeting & tell you where to take the nut back.
8) (I hope you don't get to this stage) cry when you realise you've taken the groove down as well as widened it, and now the string buzzes unless you stick a bit of paper under the string, forever.
9) Take it to the luthier to have a new nut put in.