I'm going to begin by quoting tinstar15 for this one:
FWIW, Blu/Volcano/L88b atty's and batts are cross compatible to a degree with 510's. You can use a 510 batt on a L88b atty and vice-versa. Its handy if you want a pass
through for the L88b, you can use a 510 PT. But the polarities of the
batteries for both models are opposite, so you cannot use 510 chargers on an L88b battery or vice-versa.
He doesn't mention carts, but those blu carts of yours will of course fit your blu attys, which we've just learned work with 510
batteries. I kind of doubt that the blu cart will work effectively with the 510 atomizer, or even if it will fit.
As for charging the new 510 batteries: by the time you read this, they will be fully charged, even per the manual's instructions, so I guess it is a moot point for you.

For future reference, don't worry about overcharging your batteries; they and the charger are designed so that is not a problem.
You'll get all kinds of opinions on how long initially to charge new batteries. I regard that green light going on as a minimum. Adding another couple hours can't hurt.
[Psst: When I got my first 510, I charged one of the batteries fully, but snuck a few puffs from the other battery in the meantime, because I just couldn't wait. Both of those batteries are still working fine. But don't tell the 510 battery charging police. OK?]