IMHO and from the rural property we live on:
For the gravel driveway - you can use whatever you like to kill the existing stuff in there. Glypho will work well now as its going into Spring - but you could even use salt+vinegar if you wanted on a hot day. I'd not worry about removing the dead remains, it'll decay away soon enough. Consider using a residual herbicide every 6-12mths to ensure it doesn't come back - Simazine is regarded as one of the better choices, Bunnings sell a product but you can buy better value/strength ones on Ebay or at a good Ag store.
https://www.bunnings.com.au/brunnings-1l-path-weeder_p3013486
For the weed near your shed I'd just spray with Glypho.
None of it should be an issue - just apply patience but glypho only works when the plants are growing and they will be soon.
Last edited by N1KK0; 31/08/20 01:43 PM.