a) is correct.

• South has zero defence to an opposing heart contract and a decent hand for partner, who will have six diamonds (assuming he is using the Suit Quality Overcall Test, he can’t get to eight (SQOT count) without six cards, because you have three honours); plus you have a singleton. More to the point, if you jump to 5♦ now, won’t West, who is very likely to have as yet undisclosed heart support, go on to 5♥. This might be one level too high. Sacrifice bidding in general is not a good idea, but an advance sacrifice like this can induce the opponents to bid one more, which is good (for you).
• With Hand (b), you should bid 2♠, an Unassuming Cue Bid, showing a good diamond raise.
• With Hand (c), you should gamble 3NT – there may well be nine running tricks (opposite as little as, say ♠xx, ♥Kx, ♦AJxxxx,  ♣xxx).