Hi..could anyone PLEASE list out some of the equipments that are able to reflect and deal out icons at the same time. Thanks

Put 1 as the "minimum" of icons being dealt. And then click on the "Reflect" box. That SHOULD work

I duno but, the 'advanced search' only gives a limited number of equipment.

There are very few weapons that reflect and attack, although there are a lot of weapons that can defend and attack.
Wand of the Dark Faerie, Dark Faerie Collar, Bubble Blaster, Brass Scarab
U-bend. Jhudoras Wand, Illusens Staff, Eyrie Guard Sword
There's your list. Eyrie guard sword cannot be bought by the neopian public. The only ones you can afford are Bubble Blaster and u-bend. If you're rich maybe you can afford a dark faerie collar ^_^