STEP III and Mechanics/Stats

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Just a thought, would it be unhelpful to do the STEP III questions on the assignments if you're doing STEP I and II? Also, are the mechanics and stats questions the same level of hardness throughout all three papers or (for example) is the stats in STEP III harder than STEP I?

All practice is good!

Doing the STEP III questions will not hurt (if you have spare time)- they may need some things that are not needed in STEP I or II but will still practice some of the calculus and algebraic manipulation skills that you need. Also they will give you further practice in tackling unfamiliar questions. Generally speaking the difficulty should increase over the three STEP papers, but difficult is often in the eye of the beholder...