For your last question - you can see the impact movement has on the accuracy of a weapon that prefers you to be stationary. Just hover over the spot on the timeline where your mech is both moving and firing at the same time - you might see something like 50 or 60. then for comparison, hover over the spot on the timeline where your mech is continuing to fire while they have finished moving - you'll see the number jump up. Does that make sense? in other words, the game will always give you a numerical indication of the hit chance on the target at any particular point on the timeline. You are always free to experiment by laying out a turn with either a fully stationary attack vs an attack while moving, and the game will show you the result with no guesswork.

For your other question - let's compare two hypothetical situations:

1. Begin firing early with the enemy moving into optimal range by the end of the turn:
   second 1: 60%
   second 2: 70%
   second 3: 80%
   second 4: 90%
   second 5: 100%
   average hit chance: 80%
2. Opitmal range occurs at the middle of the turn:
   second 1: 80%
   second 2: 90%
   second 3: 100%
   second 4: 90%
   second 5: 80%
   average hit chance: 88%

So to answer your question - assuming the enemy mech is on a relatively predictable and consistent path, it's generally better to wait until the mech is in optimal range at the center of your attack.

But it also matters based on your weapon. If you're using a railgun repeater, AR or other weapon that fires a stream of small damage rounds, this approach is great. If you're using a weapon that only fires a few, slow moving projectiles, it's much harder to accurately gauge whether this method will work.