What is the source of your radicals?
As to the posted reaction conditions, H2O2 decomposes under basic conditions to oxygen and water
No, not always.
35% peroxide, conc.NaOH, precipitates semi-soluble sodium peroxide as a hydrate. I forget how many hydration waters. Just needs to be kept cold.
a) acidic: protonate OH on carboxylic acid, make it a leaving group for the attack of the peroxide
b) basic : presumably a COOH is more acidic than H2O2, so COO- will be present, which would make O2- the LG, which seems very unlikely.
c)radical: unlikely.
Not sure what this OH+ stuff is....