[CIDER]: Should 10mm of foam in the presed juice affter a day be an issue?

Could be a yeast or could be lactobacilius - or both! Either way its going now and the only way to stop it is to pasteurise it. I would tend to let it go. As has been said, cider was traditionally made by crushing the juice and storing it in a vat to ferment naturally over some time. No yeast was ever bought or added. In the majority of cases the cider produced was excellent. On the other hand I have witnessed and sampled a few fermentations where the resulting "dry scrumpy" was "peculiar to the region and enjoyed by those who had a taste for it". But no one else...

After this brew has finished primary fermentation rack off and transfer to conditioning cask or bottle as preferred. It may turn out very well!

Traditionally cider is made without pitching additional yeast. There is plenty of wild yeast on the apple skin. In fact apple skin is such a reliable source of wild yeast that it's often used for making a sour-dough starter. Unless you've taken steps to kill the wild yeast that's what the foam is and that is what will ferment your cider.