Should the public be informed by appropriate notices that a road is private? Further, is it a legal requirement that private roads be barred off, at least once a year?
No.
I take it you mean to establish the continuity of it being private? - No again - it takes a lot longer than one year for a public right of way to become established.
There is a custom that some private roads are barred off once a year - often on Good Friday. But it's not a legal requirement, just an easy way of demonstrating that it's private.