So how flexible is Plate? (1300-1670, Europe) Does it restrict movement and breathing? Also when you ride in plate do you put your heels down or what?

Well designed plate armour, or at least armour that is designed for the wearer, isn't that bad. Does it restrict movement? I guess that would depend on how good the armourer is who made it.
I have a friend who made a full set of German Gothic plate armour for himself and he can do a cartwheel in the armour. Well I should say his cartwheel in armour is as good as his cartwheel outside of armour. It does hinder some movement but nothing that impairs his fighting. Its really quite good for a first attempt from a novice armour. I believe that some of the minor issue would be easily solved by a professional armour.

As for restricting breathing, well that has more to do with the helmet design. I have never had a problem breathing in armour, even wearing great helms, because of the armour. Now overheating that's the bigger issue but that has more to do with me being out of shape

I would guess that you put your heels down when riding but I will defer that answer to people who know more about riding than me.