If you want a higher chance of seeing a rare enemy you can try the pipe trick. For example, if you want to see a pal rappy then do the "Fake in Yellow" quest, find the room with the most rappies and then drop a telepipe and go in it. When you go back down the telepipe it will randomly respawn the enemies, giving you another chance to get a pal rappy. Do this as many times as you need to find one. This trick also works with love rappies, red slimes, hildetors and nar/mil lilies. Although it does require alot of patience seeing that a rare enemy spawn is around a ratio of 1/360. But if you're patient you'll get one eventually.
And to answer your other question, pal rappies do NOT always drop rare items. Like all other rare enemies the drop ratio is higher, most of the time you have a 50% chance for a rare drop. But it's like a coin toss, you do have the chance of calling it wrong 3 or 4 times in a row resulting in no rare drop.
EDIT: Thanks for the exact figure Ria. I wasn't exactly sure of the ratio.
And to answer your other question, pal rappies do NOT always drop rare items. Like all other rare enemies the drop ratio is higher, most of the time you have a 50% chance for a rare drop. But it's like a coin toss, you do have the chance of calling it wrong 3 or 4 times in a row resulting in no rare drop.
EDIT: Thanks for the exact figure Ria. I wasn't exactly sure of the ratio.