I'm wondering if you read the link that Backyardgardener gave to Lejardin about David Austin roses and if it answered any of your questions.* You don't say which ones you have that face down, but a google search with their names and + droop might be helpful to understand if these particular cultivars have that habit.
As to the petal drop, that is usually from environmental reasons such as not enough water, very hot weather or not enough fertilizer.* Also, some varieties tend to drop their petals more quickly then others.* You might want to search with terms such as:
Gertrude Jekyll + rose + petal drop
You might be able to find more info about your particular cultivars here.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.