Hi Jim
Page 35 helps you out here....
(1) Unmarked Minefields - "....the unit will take this number of attacks....Continue testing one unit at a time until either one unit is suppressed or knocked-out...". So Yes.....minefield hits test for suppression.
(2) The Effects of Minefields - "Units that fall back or retreat when they are in a non-dummy minefield are knocked out". This is also in the Reference Sheet under Fall-back.
(i) An unsuppressed unit in a minefield can be suppressed using usual fire rules.
(ii) An already suppressed unit that take further unsaved hits will fall-back and be auto destroyed.
Hope that helps
Ps ....Minefields are dangerous.