Use your infantry to screen your tanks by advancing ahead in a light skirmish line, and hold part of your armor back to provide over watch support, the other part should use mass area fire to blast every possible gun or ambush site.
Assume the worst, for it is bound to show up.
Yes, but it depends. If the mines are daisy chain they will clear them within a turn or two assuming they are placed close enough (usually within 10-15 meters is sufficient) to the mines.
If they mines are the standard AP or AT then the engineers will need a satchel charge to clear the mine, and again be within 20 meters or so to safely clear it.
Two things that have a direct effect on the clearance of mines are unit experience and enemy action. A green engineer will take longer than a regular, who takes longer than a vet, and so on. Also, if the unit is affected by enemy fire it will cease the clearing operation, so keep them in cover if at all possible. A HQ with good command and morale bonuses will help in that regard.