The way I see it, chakra works by attracting or repealing whatever it comes in contact with. As simple as that. When you try to walk on a tree or any other stagnant surface, you need to charge enough chakra so that it attaches you to the surface, but is neither too weak that you're easily rubbed off, or fall by the force of gravity, not is too strong, or it will crush the surface you're trying to hold on to.
With that knowledge, you should be able to preforms simple stuff, like walking around through about every surface you want, despite it's orientation. You can use that to gain a more tactical position, even scaling a wall to dodge some jutsus, and even counter attacking, by throwing yourself from a higher ground, or preforming a jutsu from above. This is also good to pick up weapons or loose debris from the ground, and enhance your fight by throwing those hands free. With enough mastery, you could be throwing a large amount of dust into your opponent's eyes, while making handseals, and in the very next moment, throw a kunai amidst the dust cloud, and charge it with lightning mind air, or any other jutsu, since you were free to do so. It is not considered Yin and Yang, not does it have much relevancy to the jutsu or chakra count, for it is something ordinary and you're used to it (From Ninja Academy, which we don't really have xD).
Then you have the Walking on Water technique. The way I see it, is the ability to use the attaching ability in such a manner, that it nearly automatically (This is done through time and practice which you already have, theoretically speaking). What you are doing is modulating the chakra stickiness on your feet, to adapt to the flexibility and flow of the water. Whit this knowledge, you should be able to attach yourself to moving surfaces, such as, and most importantly, a summoning animal, allowing you to ride it hand free, and automatically adjust to any rapid shifts or halts, however unexpected as they could be (to a certain extend). This will also allow you to not loose footing with most low ranked earth-shifting jutsus, adjusting to the vibration of the ground in order to remain standing. This should be a good enough counter for almost anything up to C rank, maybe even B, as long as you conscientiously regain awareness of your "Water Walking Abilities" and use it in combination with your knees to soften the impact and the vibration.
This is because, generally, even in techniques specifically meant to shake you and make you loose your footing, they are, still, something directly cause by your opponent, as such, you need to react to them, it is something "unexpected" that transcends the automation you have in your brain. Before I said you could react to them without thinking, this is because, although exterior to you, your summoning animal is something you have a certain familiarity, which you gained through extensive contact and training, but if said stops are cause by an abrupt enemy technique, the familiarity will only get you so far, and you will need, once again, have to react by showing the process of charging chakra through your feet and modulating. This can even fail if the change is violent enough, or the jutsu strong enough. Also, these do not count towards the jutsu or chakra count, but they your opponent can interrupt your jutsus by forcing you to react, and, even if you continue with your jutsus, you will still need to repost them.
As for Speed or Strength, I see them as the repelling ability of chakra. What you do is, in terms of speed, instead of attracting the ground, you're repelling it, thus, as you run, you are actively propelling yourself to move faster. In our Rp, without a technique, the speed doesn't increase all that much, but it's still enough to grant you some sort of advantage over people not using chakra, or simply lower ranked. (Or make you as fast as someone of a higher rank not using chakra). The super strength, in my opinion, is nothing more that a really high concentration of chakra being expelled from a small area, and pushing everything outwards. You can recreate this to achieve a certain increase in strength, but nothing of the scale of Tsunade, not without a technique, at least. You can also use this to throw projectiles faster and farther, by repelling them outwards. This, combined with the sticky property, will allow you to use your feet almost as well as you hand when throwing projectiles xD
So yeah, Repel and Attract, that's what I wanted you to describe xD