I get lean burn without a battery, and this is normal for an Insight. If you leave a failed battery in, it can cause lean burn to shut off (depending on the code), but flipping the switch on the IMA system or unplugging it entirely leaves lean burn intact. There isn't a lot of reason to shut off the CEL other than for passing state inspection.
Mudder over at IC posted a video on how to set it up. Basically you cut some connectors from the IMA wire harness, then connect them to an arduino. Flash the code Mudder wrote, plug it in, and you're good to go. Mudder's code disables lean burn on a small number of Insights (maybe those with older ECUs?), but I found a workaround and can have my cake and eat it too.
How to Completely Remove Your IMA Battery - Insight Central: Honda Insight Forum
As for double clutching, yes, you let the clutch out in neutral, then press it again before putting it into gear. There's one more step - when it's in neutral, you give it some gas to roughly match revs. Basically if the engine will be at 2000rpm in the new gear, rev the engine to 2000rpm in neutral before pressing clutch and dropping it into gear.
The reason this works is that the synchros in the Insight have a design flaw. They normally match internal transmission speed to engine speed when you drop it into gear. They malfunction, so the speeds don't match and the gears grind instead of coming together smoothly. If you roughly match revs when dropping from 3rd to 2nd (just blip throttle in neutral) it goes into gear smoothly because you're doing the work the synchros would otherwise be doing. And, it's only the down-synchro in 2nd (and sometimes 1st), not the up synchros or any of the higher gears.
EOC to a stop can be an issue *sometimes* with this problem. If you shut off your engine while rolling to a stop, but the light turns green and you're still moving a few mph, you can't blip the throttle to match revs and it'll grind when you try to put it in gear because the engine will be turning slower (0rpm) than the gear (more than 0rpm, since the car is still moving). My workaround is to drop it into 3rd and bump start the engine, tap the throttle, then drop it into 2nd (or 1st). If I come fully to a stop I just use my starter.
For what it's worth, I'll be fixing this flaw permanently in my transmission and selling it when I take it out of my car. One could in theory buy a fixed transmission, swap it for theirs, then fix theirs and sell it. Many Insights have had this issue fixed already too, and some don't develop it, but it's common.
EDIT: I sometimes see decent looking Insights going up for sale on IC, on Facebook groups, or on Craigslist. I'm sure something will come by if that's the route you take. I would not feel bad at all about an HCH though, they're quite solid.