You'd need to adjust it like you would a normal clock. But in theory you could make one that could do it automatically; the angle the sun is at also tells you what time of year it is.
Not uniquely. The angle of the sun (its height above the horizon at midday) tells you that you must be at one of two times of the year. Those two times have different solar time corrections.
The time corrections are based on the length of the day which is based on the angle of the sun. So it won't be perfect but it might correlate fairly well.
If you look at the bottom right part of the image, you will see that time difference cannot be uniquely determined from declination. Declination will narrow down the time difference to two times of year, which have very different time differences, but you will need some other information to determine which of the two times of year it actually is.
For example, when the declination is neutral, at the equinox, it may be the spring or autumn equinox. Those two times of the year have different time differences - one is plus seven minutes while the other is minus seven minutes.
