does exploit weakness and psychic blast and pulse wave work on a character with power cosmic team ability

All powers are available, however, Galactus has powers that cannot be used against him. You will need to read Galactus rules for those powers

figures with the power cosmic cannot have thier powers countered (i.e. what outwit does). PW, PB, and EW all ignore powers, so unless there are special rules making the figure immune to specific powers (like galactus has), they can be affected by those powers.