I'd cut it right back to a bud a few inches from the ground and cut back on the watering.
But I know nothing about roses either
I'm not sure it's rampant. It's along time since I grew it, previous garden, but I think it trailed out from a central root like some geraniums do.
It's an antirrhinum relative
only might be fidget
I thinK Pilosella is now. Or was that last week?
maybe Malva moschata or similar
are you good at description? leaf shape, flower colour, number of petals, type of flower, plants size, habitat and anything else you can think of
Have you got any more pics? I'm not really seeing persicaria there. An indication of size would be useful