They are not required. The implements add a bonus to your attack rolls and damage if they are enchanted and also offer some other bonuses even if they are mundane, but you can cast the spells as written without them.
As for whether spells can be cast with your hands full, I couldn't find any other ruling than a small mention on page 54 that the DM might rule you can't use your powers on a situational basis and the example it gives is if your hands are tied. If it written in plain english somewhere else, I couldn't find it.