Ketone to alkene regiochemistry
Part (a)

I agree with the previous comments that a Wittig reaction is the best way forwards especially in terms of regioselectivity of the double bond. PPh3, MeI and NaH would be an excellent combination. Perhaps draw the mechanism and you'll see how/why this work so well?

If you are interested, you could use (Cp)2Ti=CH2 also known as Tebbe's Reagent. Klaus Warzecha mentioned this already (above).

Part (b)

I like your idea of reducing, tosylating and using the non-nucleophilic base tBuOK