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The cyclocross tyre rule only applies to UCI ranked races, which in the UK is predominantly National Trophy Elite and Junior races, and the National Championships in the same four categories. So if you want to run 35c (or larger) for Summercross, it's not a problem and I very much doubt you'll notice any real difference in performance.
On the second point, I've no idea, but Vittoria don't do a 37c width Terreno Dry, so it's either a 35c or a 38c.
I’ve got some Terreno Drys in size 35c x 700, they’re also marked as 37-622.