I just played a game where I had that wand that always replenished your spells. What's to keep you from continually cast spells against your opponents, assuming you keep drawing spells that are of that type?
You can only cast as many spells per turn as you started that turn with. So if you start your go with 1 spell, you can only cast 1, even if you get another the same moment you cast it. This goes for out-of-turn spells too. If you've already cast your quota of spells, you can't counter another spell cast out of your turn with a counter spell.
The Spell limit rule prevents spell recycling and spells can only be cast if they have an effect - healing must have less than 4 lives, nullify must have spells, cannot cast counterspell on own spells, etc.