The statements (A), (C) and (D) are correct.
(A) I2 does not react with ethane at room temperature even though I2 is more easily cleaved homolytically than the other halogens
Iodine free radical abstracts hydrogen free radical from ethane to form ethyl free radical and HI. This reaction is reversible and occurs in the reverse direction to a greater extent than in forward direction as HI is a strong reducing agent. Hence for the forward reaction to occur, higher temperature and an oxidizing agent such as iodic acid, nitric acid or mercuric oxide is required.
(B) The regiochemical outcome of a free radical addition and an electrophilic addition reaction on propene are different. For example, when HBr is added, isopropyl bromide is added via electrophilic addition but when the addition of HBr is carried out in presence of a peroxide, n propyl bromide is added via free radical addition.
(C) The rate of bromination of methane is decreased if HBr is added to the reaction mixture. HBr is the product obtained during bromination of methane and when it is added, the rate of backward reaction increases.
(D) Allylic chloride adds halogens faster than the corresponding vinylic chloride as Cl is electron withdrawing group and the addition of halogens to alkene is an electrophilic addition.