Do you have an existing map you are trying to convert? Maps for this system would be easy with 1 square = 1 meter. There are no miles. It's kilometers.
If you are using an existing grid that's already in 5' squares then each square would be 1.5 meters for conversion. And yes, 6 meters is 20' movement. If you want 5e's 30' movement you would need 9m moves.
As long as 1 square equals 1 meter then the 20 meter range on the grenade would be 20 squares. As for the long arm, that's a long range shot and well under the current world record for a sniper shot at 3540m with a confirmed kill. Keeping that range in perspective, if the longarm is shooting over 200m with +2 proficiency and +3 DEX bonus against the same opponent in a tactical vest and tactical helmet it's AC 20. With disadvantage the likelihood of even hitting the target is low. The longarm can be upgraded with a scope to remove long range disadvantage and then the shooter would have a 30% chance to hit that AC. Then the shot would not drop the target even if it did hit based on the 20+ hp PC's start with.
The number looks good but the mechanics don't make it realistic until the attack bonus has increased and feats can increase the damage. It looks like it takes some investment to make a sniper with longarms workable.
First impression and subject to user error, of course.