Hi. I'm trying to recruit the 3 legendary dogs. What's their recruitment..

Well I can't tell you the first and last questions but the recommended one to bring to wish cave is mewtwo.lvl1-10,=OMG ITS SO EASY TO LEVEL
11 and above=hmm lvl 30 or something...lvl 99 WORTHS OF EXP?!?

1): 0.1% for ALL THREE! ! !
2): his normal R-rate is - 10 without ANYTHING attached! But, with a lv. 90 or higher Pokemon HOLDING the Friend Bow, (RANKS DON'T COUNT!!!) is 24.5%!
That means you have a 1 to 50 ratio that you'll recruit him every 10 times you encounter him!
3): NO, he is 1*! And yes you can recruit him with articuno cuz: articuno is ONLY 4**** which means you can still recruit 2 MORE 1* Pokemon in any dungeon,or 1 2** Pokemon in any dungeon!!!
4): well, their is really no " BEST " poke to bring! But, i'll type up a list of good ones:
Alakazam: because he has VERY HIGH sp. Defense and defense when first entering,but later on, he'll prove somewhat useless because of low attack! Be warned!
Charizard: has heat wave, ember, growl, and leer when first entering! And, has powerful attack and OK HP!
Mew: because of VERY excrutiatingly HIGH Stats EXCEPT HP!
Electrode: has sonicboom at first enter and learns AGAIN at lv. 15! It's good because it does 55 SET DAMAGE!!! That's VERY ultimately high in lv. Dungeons!
Ok, now here's some useful items to bring for joyous tower and wish cave(can't bring in items or money in purity forest!):

2 Frustration TM's because they do 45 set damage NO MATTER WHAT!!
3 joy seeds
8 Reviver seeds or more, YOU decide!
Pass Scarf

5): Snorlax is in Howling Forest, Floor 12 - 14! But, don't look in floor 12 because you're NOT very likely to find him there! His R-rate is 10%! So, with articuno,and all extras added, his r-rate will be a 44.5% chance he'll join you!
And look in floor 14! Bring a tight belt because you'll have to search for maybe 55 mins for him to appear! His chances of appearing on " Floor 14 " are 2.44%! NOT MUCH AT ALL!!!!! OMG! So, just sit there at the stairs on floor 14, with the tight belt HELD by articuno,and friend bow at the ready, then when you see him, hurry and SWITCH the Tight Belt for the Friwnd Bow and hope to god you'll get this 4**** prized one - of -kind monster! Hope I helped! - Pimpblue

Hey pimpblue! You said Snorlax is 4****? So I CAN'T recruit him with Articuno, 4+4=8 & 8>6!!!

No, you canNOT recruit him with Articuno, a 4 * body size pokemon!
Snorlax is a 4 * body size Pokemon SO, the maximum * body size Pokemon you can have on your team is a 2*! Like feraligator, or charizard,which BOTH are 1*! And REMEMBER: skip all floors until you get to floor 14! Because I gaurantee you WON'T find him in the prev. Floors he's supposed to be on : 11 - 14!
Bring a friend bow and attach to a lv. 80 or higher Pokemon when you SEE him!but if you don't see him yet, KEEP ON YOUR Tight Belt! You'll need all the belly you have! so don't bring articuno!