Weeding and bedding plant removable

Hey all, just a continuation of my thread in Beginners, but how would i safely and effeciently go about getting rid of mass bedding plants left to go out of control, and also weeds that have gone crazy from inbetween paving slabs?

Whats the best way to pull them out and make sure they're gone for good so as not to make a mess of the new planting going on top?

Should i refill inbetween slabs with some kind of cement/sand/gravel?

Heres a photo of part of the area i'm tackling in case it helps!


Thanks for the help!