The annoying broadleaf weed is Common Mallow. Get ground damp and pull.
Pointy leaves, purple flowers and dense seed puffs is Canadian Thistle. Paint leaves with herbicide.
The succulent in the cracks and edge of the grass is Purslane. Easily pulled when young.
The quick growing vine that climbs fences and plants id Bindweed. Paint with herbicide.
It looks like the clover looking weed with dark leaves too is Black Medic. Easily pulled from damp lawns.
Lawn care fact sheet.
The “paint leaves” is where you want to keep the underlying or surrounding vegetation. For gravel or fence, just spray. The blue Bayer stuff works well.