In this sentence, uva is grammatically singular, even though in English we translate it as grapes.
Italian often treats foods like this as a mass noun:
You can find uve, but that usually refers to different kinds of grapes or is used in more specialized contexts. For everyday speech about eating grapes, uva is the normal word.
In spiaggia is the normal Italian way to say to the beach / on the beach, especially when talking about going there or being there as a place/activity.
So:
Using alla spiaggia is much less natural in standard Italian in this context. Learners often expect a direct equivalent of English to the beach, but Italian usually prefers in spiaggia.
Yes. That word order is also possible.
Italian word order is often more flexible than English. Both of these are natural:
Starting with A Ferragosto gives a little more emphasis to the time: On Ferragosto, we bring fresh grapes to the beach.