Charging the lithium battery with higher rated charger
What happens if lithium cells are connected to a higher current capacity charger? Say, a 10Ah 1C rated cell is charged with a charger of 20A. Would the battery only take the amount it requires and leave the rest alone?

Nothing good happens. The cell will be charged at 20A until the voltage climbs high enough to initiate the CV portion of the charge cycle. Short cell life can be expected. Cell temperature will likely be pretty high, also. And cell death cannot be ruled out.

What happens when the lithium cells are in a pack? Say a 48V (13s8p) is connected to a charger of 20A? Would the load be shared by 8 parallel cell joints?

Yes. The current will be shared. Not necessarily perfectly equally, but assuming the cells are all the same type and age, it should be fairly equal. Do not assemble high discharge rate packs from multiple cells unless they are exactly the same, from the same order and batch.