That’s not cadence, you’re still in the figuring-it-out stage. Cadence will come later, when you can decide how fast you want to go, and are able to go that speed.
I don’t remember your wheel size, but at this stage, I don’t recommend going shorter. Shorter cranks take more power to push, which will delay the reaction you need, and end you up going faster than you want, if you haven’t already fallen off by then. For now, leverage is your friend.
It’s okay if you still spend a lot of time at the wall; it’s different for kids and teenagers that can bounce up from an unlimited number of dismounts and falls. But treat each dismount as a learning experience. Analyzing why you fell off will help you figure out how to do it a little differently each time.
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So I am practicing idling more, hoping that will help me get tuned in.
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I don’t know that idling will help with leg reaction speed, but it teaches you the power transfer of changing direction, pedaling past your point of balance (over and over), and is the gateway to freemounting and riding backward (save those for later). Your goal in idling is also to learn the side-to-side motions necessary to keep the wheel under you. Also to not rush it. Idling can be done pretty slowly once you learn how to do it. Performers do it fast and exaggerated, to make it look harder and more sketchy.
Probalby not, yet. But it proves you’re putting enough weight on it to be annoying, and that’s a good thing. 
I’m not a fan of learning on grass; it really depends on the quality of your grass. It tends to be very unpredictable underneath, and more work to push the wheel through it. But in exchange, you get a much friendlier surface to fall down on.
Good question, as it’s important to not take all your support from the same side. This will teach you to basically ride in circles toward that side, and have a much harder time learning to turn the other way…