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>Is it just the difference in daylight?

Yup, many plants have competing chemical processes triggered by light, darkness, and the wavelengths of light you tend to get in the morning/evening. As the days get shorter this balance shifts and trees leaves start to change color.

>If so how does the tree grow in the spring with similar day lengths?

Plants have a few different strategies here. Some plants do need cold here, as the cold will open access to a gene that was closed off during the fall, allowing them to flower when they days get longer again through a process called vernalization. It is pretty well studied because it occurs in the plant model organism (thale cress).

I am not much of a horticulturist, so I am sure that someone can probably give a much better overview of the different strategies.

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As far as your other questions, it's probably a more complex interplay of triggers including both day length and temperatures expressed in what are called degree days.

https://en.m.wikipedia.org/wiki/Degree_day

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The leaves of trees change color in the fall because the tree is no longer producing chlorophyll, which is what gives leaves their green color. The green color of chlorophyll is due to the presence of a pigment called chlorophyll a. Chlorophyll a is essential for photosynthesis, which is how plants convert sunlight into energy. In the fall, the days get shorter and there is less sunlight available for photosynthesis. As a result, trees stop producing chlorophyll and the green color fades from their leaves. The other pigments in the leaves, such as carotene and anthocyanin, become more visible as the chlorophyll fades. The different colors of fall leaves are due to the varying amounts of these pigments present in the leaves of different tree species.