It looks like your lavender has died back on the right and left. I don't know why, but you might as well cut those parts off. The middle looks nice and green, though, so I'd say the plant is okay. I have never had a lavender that rebloomed, but maybe some kinds do; hopefully someone more knowledgeable about them will chime in. IME, lavender likes good drainage more than anything else, and the presence or absence of mulch doesn't make much difference. Stick your finger in the soil and make sure it's not sitting with wet roots.

As to B - it looks to me like a young mugwort, which is not a good thing at all. I could very well be wrong,though, so you may want to take a closeup of just that plant and post it on the Name That Plant forum, as the people who answer there are magical.