1. Heavier BBs tend to give greater accuracy and longer range.
2. Yes, if it is locked to semi, although you would be very close to the limit. Bear in mind that not all chronos read the same so you could end up not being able to use it if the site chrono reads higher than your one.
3. While power has an impact on range, a high quality barrel (not a Madbull Python!), hop unit, rubber and nub are vital, as is ensuring that you have excellent airseals and that the barrel and cylinder are properly matched. To push the power up to 1.87J, you need to fit a stronger spring; to pull back that stronger spring, you are almost certainly going to need a high torque motor. However, there is far more to setting up a DMR than that.
Your site is sensible in using Joules rather than FPS; 1.88J is around 450 FPS using a 0.20g BB.
Impulse gave you good advice.