Gathering Speed resource when do I use it, before going on plots or after or doesn't it matter?

I don't think it matters. I have used it towards the end of a gathering period and it has sped up the process.

This tip is risky but if you are able to gather During Sunday and into Mondays Gathering Event you wait until the event starts. Pop a bonus score token then use your gathering Bonus. For maximum benefits.

Otherwise if you are just gathering on any random day it wont matter