Question: Lately I've started learning some basic music theory and I have been trying to rationalize some of the interesting chords I have heard of from famous pieces. Here is an example of which I am not sure if my understanding is correct.

Below are bar 11-12 from Mozart's Piano Sonata No.11 in A major, K.331. I have marked the chords using Roman numeral notations.

[![score](https://i.stack.imgur.com/Px8LY.png)](https://i.stack.imgur.com/Px8LY.png)

The blue text shows a naive marking. To me the ♯iv° chord gives a warm and sweet shifting feeling. I found that if I think of it as an applied chord (by tonicizing V) then the last three chords becomes a (vii° - IV - I) progression. If this is the case I was wondering how come the IV chord, as a pre-dominant chord, appears *after* the dominant chord vii° instead of before it? Why would the progression still sound inevitable when the strong dominant -> tonic progression is broken? 

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Per @Dekkadeci's answer I revised the analysis as follows. The final three-chord progression simultaneously resolves two tension (cadential I chord to V, and on the V scale, dominant vii° to tonic I.

[![score2](https://i.stack.imgur.com/mf2pZ.png)](https://i.stack.imgur.com/mf2pZ.png)

Answer: 
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> If this is the case I was wondering how come the IV chord, as a pre-dominant chord, appears after the dominant chord vii° instead of before it? Why would the progression still sound inevitable when the strong dominant -> tonic progression is broken?
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Due to the E as a root instead of an A, the second last chord is not formally a I or a plain IV/V chord, but it is actually a I 6/4 chord. The I 6/4 chord is treated as a pre-dominant chord that must be immediately followed by a dominant-function chord (often V, just like the last chord). Its pre-dominant function is so strong that one of the theory books I was told to use in harmony class labels it as V 6/4 instead.

(I also believe that the "#iv° 6" is actually vii° 6 of V.)
The second chord could easily be the leading tone chord with the E functioning like an escape tone. That big jump up and the step down is typical of an escape tone.

The d sharp that resolves to an e in bar two gives the very real impression of a leading tone resolving, Im thinking E major. The notes in the top two voices of the last beat just look like suspensions from the previous beat