My viewpoint

Most of the time, eg for phone cells, the recommendation is to stay at or below 0.7C - also, when you hit 4v, the last 200mV is done in constant voltage mode, so the charge current will taper toward zero and hence you're charging a lot more slowly towards the end. This tends to work out to be in the 2-2.5h range for a full charge.

Often the charger will determine "finished" when the current into the battery falls below C/20 (0.05C). Charging beyond that point - continuous trickle - is bad for the cell in the long run. Any Li-Ion charger should be stopping charge when the charging light goes out - no trickle.

As for the battery being 2/3rds or so full, that's how Li-Ions are shipped. Their shelf life is best when at about 2/3rd capacity so that's how they leave the factory. It's not a "surface charge" and is totally valid usable capacity.

Lastly, never charge below 0C or above 45C. Charge at 20C or above if possible, or lower the charge rate if you can't.