I think Daily Writing Practice will help Improve Writing Speed.
Students who attend Coaching classes, Write NOTES/running Notes, so usually Their WRITING SPEED is much Better.
Writing short Notes of Editorials/ Essay TOPICS etc will help in Improving Writing Speed.
We have to write at-least 3 hrs/day DAILY for at-least from 1 month before mains.
Solving Mock Mains Test Series Will be MUCH Helpful for TIME MANAGEMENT.
On exam day, Before entering exam hall Take an Rough SHEET and keep writing anything for 10 mins so that your hand will Get Better Warm Up. (This seems like a Joke but practically it works)
Coming to Pens, Pilot v5 is Best one or Any SIMILAR Pens will be helpful in Writing Faster. (My Opinion)
(PinPoint Pen is also equally Good)
Wish You ALL SUCCESS