IP65 charger connected to battery whentheris a 10 amp load

I have a 12v oven connected to a LiFePO4 battery which draws 10A when switched on. My IP65 12/15 charger is also connected to the battery. When I have shore power can I switch on the charger at the same time that the oven is on? If so should I leave the charger on the Li-ion charge mode?

Yes you can

and yes you can.

Power supply mode has a lower voltage than the battery voltage (depending on how depleted it is of course.)

Thanks