This is incorrect for a number of reasons.
SN2 reactions result in complete inversion of stereochemistry, not a racemate. That means that if this reaction were SN2, you would only see one stereoisomer and not the other one.
The sterochemistry of the carbon with the deuterium attached doesn't change its configuration. It's ® configuration in both starting material and product. The carbon that actually underwent substitution, however, is racemic. See:
The carbon with the deuterium attached to it is not the carbon that gets attacked. If it were, you would not expect the other carbon centre to undergo racemization.
You need to write more clearly. I couldn't understand a word of the last part of your post.
One of the key differences between an SN1 and an SN2 reaction is the way they effect stereochemistry. In an SN1 reaction, your leaving group is eliminated fromt he carbon undergoing attack to generate a carbocation intermediate. These types of intermediates are flat structures and attack from either face will result in a different steroisomer:
Image from http://www.organic-chemistry.org/namedreactions/nucleophilic-substitution-sn1-sn2.shtm
Because they are flat, an incoming nucleophile will attack either face of the carbocation without any preference, thereby resulting in an equimolar mixture of both ® and (S) isomers (i.e. a racemate).
SN2 reactions do not undergo the same mechanism and result in an inversion of stereochemistry. The analogy I was taught in undergrad is to think of it as being similar to flipping an umbrella inside out.
Image from http://www.organic-chemistry.org/namedreactions/nucleophilic-substitution-sn1-sn2.shtm
You need to think about this some more. Why would the carbon act as a nucleophile and pick up a proton? Since you know that this is a substitution reaction, the first things you should be trying to identify are:
The electrophilic carbon centre and whether it is a primary, secondary or tertiary centre.
The nuclophile.
The leaving group.
In this case, the electrophilic carbon (i.e., the carbon being attacked by the nucleophile and which undergoes substitution) is one of the benzylic carbons attached to the aromatic ring. Both are secondary centres, which you would typically say could undergo either an SN1 or SN2 reaction. To figure out which of these is occurring, you only need look at your products. Since you have a racemate, it must have undergone an SN1. The reason for this is because the carbocation intermediate is able to be resonance stabilised by the adjacent ring.
Looking at your products, you should be able to see which carbon has changed in its stereochemistry and therefore, which carbon was attacked by your nucleophile.
This is not in any way correct. You are dealing with a simple substitution reaction, certainly not a hydride shift or anything else. You need to break this down and look at it step by step. Firstly, can you identify what your leaving group was? You're right to assume that the acid has done something, but you have not correctly identified what that is. Have a look at your starting material and try to identify which atoms are capable of donating a pair of electrons to pick up an extra proton. Hint: it's not the carbons.