1) If you don't bind a spell, then you can only bind a spell if the ability of the card lets you bind a card later. For example, you must bind a spell to Thoughtspore when you cast it if you want it to ever have a spell bound to it. You can't bind a spell to it later. Wizard's Tower, on the other hand, can change the spell bound to it every upkeep. Mage Wand and Elemental Wand can bind a spell later on, but it costs you mana and an action, as indicated on the cards.
2) You cannot have more than 1 card with the same name attached to a single object. This applies to equipment, enchantments, and conjurations. You can't have 2 Dancing Scimitars or 2 Bear Strengths on your mage.
3) I have not. Apparently there is a promo card for the Wizard that lets you do that, but I haven't played with it. You don't always cast both spells you select anyway, so you can often set up a choice of what to do with your turn based on what your opponent does. There is plenty of room for tactical play in the game as it is, and normally only getting 2 cards forces tougher choices up front (plus it makes play faster, since you are choosing fewer cards per turn). I think the system works fine as it is. Also, some mages have innate spells that act as a pseudo 3rd card in hand, like Arcane Zap.