请正确解答图片题目---**Problem 17**
(This problem is worth 15 points) [Jiangsu Nanjing 2024 High School First Year End of Term Exam]
Known function $f(x) = A\sin(\omega x + \varphi)$ ($\omega>0, A>0, |\varphi| < \frac{\pi}{2}$). A part of its graph passes through point $(0,1)$, as shown in the figure.
**Chart Description:**
* **Type:** Graph of a trigonometric function (sine wave).
* **Coordinate Axes:** X-axis and Y-axis are labeled. The origin O is labeled.
* **Graph:** A curve representing the function $y=f(x)$.
* **Points on the Graph:**
* The graph passes through $(0, 1)$ on the Y-axis.
* The graph passes through $(-\frac{\pi}{12}, 0)$, $(\frac{5\pi}{12}, 0)$, and $(\frac{11\pi}{12}, 0)$ on the X-axis.
**(1)** Find the expression of the function $f(x)$;
**(2)** Shift the graph of function $y=f(x)$ to the right by $\frac{\pi}{4}$ units of length to get the graph of function $y=g(x)$, find the range of values of $y=g(x)$ on the interval $[0, \frac{\pi}{2}]$;
**(3)** If $f(\alpha) = \frac{2}{3}$, $\alpha \in (0, \frac{\pi}{2})$, find the value of $f(\alpha - \frac{\pi}{4})$.