If I backdated an Inventory Adjustment and changed the rate, will netsuite change the GL impact transactions after that date? Can I trigger a revaluation of the GL impact manually?

It will trigger calculations automatically or when inventory costing is scheduled in your account. It will fix the COGS on transactions affected by new costing calculation.

Any way to trigger an inventory costing manually?

Yes try to close the period there will be a task on the period close checklist to run inventory costing.

I clicked "Run Inventory Costing" but the process still says "not running"