SN2 vs SN1 in Acidic Environments for Secondary Alkyl Halides I have researched three books: Brown's, Solomons' and Wade's. I could not find enough information about this.

My prof. says that secondary alkly halides undergo SN1 only under acidic environments.

We had this quiz. I got a terrible mark on one question.


I think these are the missing structures.



Now, I am wondering, did Sn2 occur here, if yes, at what rate? Was it more important than Sn1? What was the major pathway?

What is the major pathway for all secondary alkyl halides with acidic environment and with NONacidic environments?

Could anyone also just check my missing structures?
Note that the starting material is drawn as a chiral molecule.  Solvolysis of this starting material will generate a symmetric, achiral, allylic carbocation.  Since a stabilized allylic carbocation is generated, the mechanism likely proceeds through an $\ce{S_{N}1}$ mechanism. 

Both ends (there is positive charge delocalized at both ends of an allylic carbocation - draw the resonance structures and convince yourself)  and both faces (top and bottom) of the allylic carbocation can capture the nucleophilic solvent molecule to restore neutrality as shown below. This results in the formation of two diastereomers of the 3,5-disubstituted cyclohexene - the cis and tran isomers. For each diastereomer, both enantiomers are also produced, as they must be, having passed through an achiral intermediate.