Is it the same level of gravity in all the places on earth?
No.Gravity is lowest near equator and as you move towards poles, it gets stronger.The reason for this is that the poles are nearer to the centre of the earth. With decrease in distance, gravitational pull becomes stronger.The standard value of g=9.8 m/s^2, is the value of g midway from equator and poles.
On the surface, it's 10 Newtons per square metre; however, the pressure increases as you go down, so on mountains there'll be less gravity, while deep under there ocean there is more. Does that make sense?
Yes. 9.8 m/s everywhere.