$解：(1)由题意，得∠COD= 90°.因为∠DOE=m°，$
$所以∠COE=∠COD-∠DOE= (90-m)°.$
$因为OE平分∠BOC.所以∠BOC= 2∠COE =(180-2m)°，$
$所以∠AOC= 180°-∠BOC= 2m°.$
$(2)∠AOF+∠DOE=60°.理由如下：$
$设∠AOF =x°，∠DOE= y°.$
$则∠COE= (90-y)°.因为OE平分∠BOC，$
$所以∠BOE=∠COE= (90-y)°.因为2∠BOE=3∠AOF+∠DOE，$
$所以2(90-y)=3x+y.$
$所以x+y=60，即∠AOF+∠DOE=60°$
