Yes, and in fact several Equip Spell cards would be useless if they could not, such as 'Snatch Steal' and 'Mark of the Rose'.
Chat with our AI personalities
No, the Equip card stays on your side of the field, and is under your control.
Same as when you use a regular Equip Spell card on the opponent's monster, the monster acting as an Equip Spell Card goes to your own S/T zone.
No, face-down monsters cannot be equipped.
yes you can equip spell card cards to an opponent's monster unless the card states so a good example of this is snatch steal
Yes. Cards like 'Snatch Steal' would be useless otherwise.