The subclass is mostly good from an equilibrium point of view. It lacks proactive play and, for that reason, it will probably be considered a good class for players with little or no experience, while more experienced players who want more options and active features will leave them aside for other (more proactive) classes.
I will go little by little.
It may not look like much compared to the 5-finger punch that explodes the heart of the open hand
Being honest, I do not think the Open Hand is dominated or even the strongest Monk subclass. Drunken Master and Long Death are at least as strong, IMO. Therefore, I think that comparing it with Open Hand is a fair comparison and it will be our metric.
Let us begin.
In level 3, Open Hand gives you the possibility, when using Flurry of Blows, to force some negative effect on the enemy (inclined, throw or take away your reaction).
You can choose your unarmed blows to inflict abrupt damage instead of charging.
While this has a certain flavor, it lacks mechanical sense in virtually any scenario.
You gain climbing speed equal to your walking speed.
I'm also not sure how useful this will be. Climbing is an essentially difficult terrain as it is written in 5e, that is, it would have half its speed as the speed of climb usually. With this feature, you can climb twice as fast, which is relevant if you're climbing high places in combat … I'm not sure how often this should be relevant. In my adventures I can not remember once that this would have been useful.
Also, at level 9, the Monks essentially get this feature anyway.
When you are prone, stop using only 10 feet of your movement.
Being knocked down is not so common either. I can see that this is used more frequently, but I still do not see the real relevance of it.
In addition to the bonus granted by its movement function without armor, its speed increases by 5 feet. Your speed increases by an additional 10 feet when you reach level 6 (+15 feet), level 17 (+20 feet).
It's rare for any creature to outperform a Monk anyway, so I do not see this feature as highly relevant. That might It helps in some specific scenarios and it can be interesting if you're playing, for example, a halfling who has a base velocity of only 25 feet.
So, for a level 1 adventure, this subclass seems to have little power, particularly because the features seem to be mostly irrelevant or simply too situational.
While it's hard to get additional skills and experience, I'm not sure I want my level 6 function to have additional capacity. I would rather have that if I were playing a Rogue or Bard, which are usually the "skill monkeys" of the party.
On the other hand, as I said, Open Hand would be a fair comparison, Wholeness of Body is not impressive either. I would call it a tie here. I do not think any of them is a necessary characteristic or a completely bad feature.
As a side note, after reading Cubic's answer, I do not agree that, compared to the ability to heal once a day, gain additional skill in the skills (or, more likely, the way in which the I would use (experience in a single skill) is more boring.
The advantage in Dex Saving Throws is usually good. Compared to the peace of Open Hand, it certainly seems better, being honest. But tranquility is, IMO, a bad feature, possibly the worst of Open Hand. Dex saves are one of the most common and important ST (throughout Con and Wis), and are completely free!
Even compared to Drunkard's Luck, this is a fair feature. While the Drunken level 11 function can be used to cancel any disadvantage (attack, check or save), it can only be used to cancel disadvantages (without giving an advantage) and requires 2 ki.
On the other hand, I now agree with Cubic's claim: most of its functions are now passive. You are giving small choices day by day. "When to use this feature?" It is a question that none of your characteristics raises.
Well well. Now I see your point. The trembling palm is stupidly strong. Period. Yours is similar to Drunken Master's intoxicated frenzy, which is also fine.
but nevertheless, he needs some extra way for the monk spend your ki points Apart from those who receive from the base class. This happens mainly due to the lack of active skills. Monk is already a martial class, which means he gets comparatively fewer options and activity than spell casters. There is not inherent problem with that. Champion does essentially the same for the Fighter class. The immediate consequence is, at least from my experience, that the class will be more chosen and appreciated by the beginning players, and will not be interesting among the more experienced players. If that's okay for you, your class should be fine.
Additional justification for "The subclass is well off a POV balance"
First of all, I do not think that a homebrew subclass has to be as good as the best subclass to be able to play. It just needs to be … playable.
That said, one point that comes from my experience with the Monk class: the most useful and interesting features are actually from the base class for the Monk. The disarmed defense allows a fairly high AC, even at low levels, Martial Arts provides your DPS, the Missile Detour is useful when fighting enemies from a distance, Stunning Strike is pretty good, Ki-Empowered Strikes allows your blows to hit the enemies with non-magical resistances, etc.
Maybe for that reason, my opinion (based on my monk players and the monk I've been playing recently) is that the subclasses are generally disappointing anyway and "even" the proposed subclass should be fine, since it provides some usefulness additional to a class that already has a good base of utility.