Leaving the phone on its charger can produce heat that can weaken your battery in the long run. So if you plan on leaving it on the charger then I would suggest turning off the phone while it charges. Just something I have read multiple times about mobile phone batteries.
Wrong. When the battery gets close to full charge, the charger shuts off completely. No more charge, no heat. If you leave it turned on while on the charger, the battery will gradually run down. At some level of discharge, the charging circuit will kick in again, until the battery is close to full charge, when it will stop charging again. This is all very well documented.
What you describe hasn't been true of cell phones for many years.
What WILL get the battery quite hot is if you're running something that drains the battery heavily (e.g., running GPS Navigation, Pandora and 4G all at once). But that's what the phone is designed to do. It'll reduce battery life somewhat, but since you can get batteries for $5 each, it's hardly a major concern.
The only issue is that it won't have a "full" charge when you unplug it. You'll see a rapid 10% drop or so. The phone doesn't trickle charge once reaching full like most phones do. It'll show 100% when you unplug it and then drop to 90% within minutes. You can unplug it and plug it back in 30 minutes before you leave or so and it'll charge back to full.
This has nothing to do with leaving it on the charger. If you took if off the charger as soon as it was fully charged, the battery would drop the same amount over time. An example: Let's say you plug the charger in at midnight, and the battery is fully charged at 2:00 a.m. If you leave the phone on and the charger connected, the phone runs off the battery until you unplug it, say, 6 hours later. But if you unplug it at 2:00 a.m., as soon as the battery is fully charged, the phone, umm, runs off the battery until 8:00a.m. IOW, it'll use exactly the same amount of battery whether it's plugged in or not.
If you do not take it off right away, you will see the huge 10% drop in a matter of minutes, even with light usage.
See above paragraph.
Leaving it on charge all the time will diminish its capacity more than keeping the battery at or near 40% for the majority of its life...
Truth, but difficult to deal with in normal usage. LI batteries don't like beeing overcharged, and don't really like being fully charged. Nor do they like being fully discharged. Cars with LI battery packs (like the Volt), maintain the battery pack between 25% and 75% to maximize battery life. But the battery pack in a Volt costs something like $20,000. Keeping that alive for a long time makes sense. I'll put up with buying a new battery every 12-18 months in exchange for not worrying about it on a daily basis.