"Friendship is one mind in two bodies." -Mencius
Tanemon is the In-Training form, whom Mimi meets in the first episode. Tanemon is the In-Training Digimon that we get to see least (bar Nyaromon ^^;), which is a shame 'cos I think she is easily the cutest. ^_^.
'Tane' means seed, or the stone from a fruit, which is pretty appropriate.
Tanemon has a similar voice to Palmon's, and seems fairly good-natured and similar in personality to Palmon also. She digivolved in the first episode to battle Kuwagamon. Her attack, like all In-Trainings, is a bubble blow.
Palmon, the Rookie, is the form that Mimi's partner stays in most of the time. Palmon is a little more easy-going and down-to-earth than Mimi, to balance her partner's more excitable personality. However, like Mimi, she can be a little ditzy, and is fairly cheerful, sometimes a little theatric.
She has a lot of patience and is good at dealing with Mimi - although perhaps it is not patience as she does not seem to be annoyed by Mimi. She did become angry with Mimi when the girl turned princess and tried to forget her friends, and called her a spoiled brat - although she did add that it hurt her to say it, and that she liked Mimi more than anyone else did. Palmon is very nice.
I think at first, although she appreciates her green pal's friendship, Mimi doesn't recognise the extent of how good a friend Palmon is - because Mimi doesn't see anything wrong with her own character, she doesn't realise what a faithful and patient friend Palmon is being in simply dealing with her the way she does, edging her closer to being a better digidestined.
Palmon is also quite the team player; she gets along with everyone pretty well, being nice and easy-going. She was one of two volunteers to infiltrate Myotismon's castle. She has a good sense of fun, and seems to get along with Gomamon best out of the other Digimon.
Palmon's name, I'm not sure, but I reckon it's meant to be from English, either "pal" or "palm", I'm tempted to think the latter, despite the pronounciation. Her attack is Poison Ivy, which is a very useful move, and she tends to use it for practical purposes rather than in actual battle.
Poison Ivy involves Palmon's arms extending to form long, strong vines of ivy. With these vines, she can latch onto things and swing like Tarzan, grab things, or hold an enemy down so that others can attack without it escaping.
Being a plant, Palmon likes dirt and soil (bit of a contrast to Mimi ^_^.) and sometimes sticks her roots (her feet) into the soil to get nutrients from it.
Palmon is always there to reassure Mimi, to protect her, and to stick up for her. Mimi did not seem to be such a good friend in return. I think she was a little embarassed of Palmon - Palmon is probably not her idea of cute. She once implied that Palmon was in bad taste, after hiding the Digimon from her father, and when they first met, she seemed critical of Palmon's hair. (I wouldn't call it hair. I'd call it leaves. But hey...)
But then, this is probably part of Mimi's growing up and learning to be more sincere (rather than judging by appearances). After Togemon becomes Lillymon - who is undoubtedly a cute/pretty Digimon and one that someone like Mimi would think really cool - Mimi regretted her words, and I think Lillymon was glad to have become something that Mimi would like. Mimi even abandoned/forgot Palmon in her excitement to be with her old friends from camp.
Generally, though, the two make a good pair, and are more similar in personality than most of the partner groups. I think that's necessary - if Mimi had a very down-to-earth and serious sort of Digimon, there might be a lot of tears and lectures and arguments. And perhaps that sort of Digimon could have gotten her to grow up too, but not as painlessly as Palmon did.
Palmon learned to digivolve into her Champion form, Togemon, in the episode "Togemon in Toy Town". She fought Monzaemon and punched the black gear right out of him.
Togemon is a cactus. Mimi seems to have something of an affiliation with cacti in general, actually. Her Digimon is a cactus, she wears a cowgirl outfit (cowboys sort of associated with the desert and cacti), and her crest was found in a giant cactus.
Mimi can only ride on Togemon if her Digimon actually carries her; the boxing gloves being the only safe part of her body to touch. ^_^; Togemon is solidly built and rather ungainly.
'Toge' means 'thorn' or 'prickle'. Togemon's attack is Needle Spray wherein she spins her body around, releasing lots of needles that spray out at the enemy. As she is a strong sort of Digimon (ie relying on simple physical strength more than agility, attack power, etc) and wears boxing gloves, she can also deliver a mean punch.
Palmon's fully digivolved form, Lillymon is the pretty fairy-girl who brings new meaning to the term "flower power"! (Hey, that sentence should be in a Digimon guide or something. ^_^.) Confident, cheerful, bright, and a little playful/teasing, Lillymon is actually smaller than her Champion form. When she digivolves it is almost as though she escapes from Togemon - Togemon's flower unfurls and she comes from it. Perhaps this is not a bad definition OF digivolving - a new power escaping from the previous digivolved's form. She is quite different from Togemon, being quick, dainty and graceful where Togemon is... not. ^_^;;
Her attack is Flower Cannon, in which she unfurls a flower from her arm, reels back in the sky, and shoots a great beam of energy from the flower. (The flower, according to Myotismon, is a geranium. ^_^.) She digivolved to fight DarkTyrannomon, who was terrorising the city, and injured Mimi's parents. Mimi was desperate to be able to do more, and the sincerity of that wish inspired her crest to react.
Myotismon called her a "power child", which I thought was a cool title for her. Lillymon can also manipulate flowers to an extent, and created a wreath of flowers that had the power to negate evil energy and neutralise viruses.
Being the only fully-digivolved Digimon not big enough to be ridden by her partner, if Lillymon wants to transport Mimi, she has to hold her by the hand and fly with her dangling there. Once, she was carrying Mimi in this way but could only perform Flower Cannon with her arms free, so she threw Mimi like a boomerang, fired her attack, and then caught her again. Mimi did not appreciate this. ^_^;;
I think Lillymon is a really, really cool Digimon. She's cute and her voice and personality are great.