1) The OED has examples from 1523 and says 'derivation unknown' but it occurs as a place-name element and Smith considered it to be a form of head, via Middle English <i>haved</i> (PNWR2/253). It was used of unploughed land in the open field, but was evidently distinct from headland.
1577 all the hades, balkes, headlandes, horsegates, beastgates, pingles, pastures and fedings, East Newton, Holderness
1617 arable lands, leys, meadowes, pastures, hades, flattes ... in the severall fields of Skerne. Note: 1642 to have an eye to the heads, balkes, and divisions that lye betwixt two faughes, Elmswell.