That cool little function is only available in gen II so unless you are playing games of that gen, the answer is no.
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Shuckle can only make rare candies in gold/silver/crystal.
If you give them a oran berry, it will eventually turn into berry juice by a certain amount of steps. if you can keep the shuckle from using the berry juice, then after another amount of steps ( i have no idea how many) it will turn into a rare candy
with some AR codes.
Yes there is rare candy in pearl
There is no stone but you can use a Rare Candy. That will make it go up 1 level, or you can get a Super Rare Candy. 1 in 100 games of Diamond, Pearl and Platinum have it replaced instead of the normal Rare Candy. Super Rare Candies make your Pokemon level 100 straight away, no matter what level they were on before hand.