please answer all parts, here is some help:

When swinging along a circular path, the elf experiences centripetal acceleration which is directed straight towards the center of the circle, i$.$e$.$ along the rope, or in the same direction as the tension. For all $3$ tension calculations, stick with the tried and true method of Newton's $2$nd law $-$ the net force on the elf in the direction of the rope must equal the mass times the acceleration in the direction of the rope.$$ And the acceleration in the direction of the rope is the centripetal acceleration. Depending on the orientation of the rope, the net force in the direction of the rope may be just the tension, or it may also involve the force of gravity.$$ But either way, writing the equation of Newton's $2$nd law should allow you to solve for the tension.

On the energy calculations, consider that if we define the lowest point on the swing as a height of $0,$ then the total energy at the lowest point is just the initial kinetic energy, determined by the speed that was given by the initial push.$$ As he goes up he gains gravitational potential energy, but to maintain the same total mechanical energy, he must lose a corresponding amount of kinetic energy.$$ If you figure out how much kinetic energy was lost, you can figure out how much kinetic energy remains at any given height.$$ From the remaining kinetic energy you can calculate the speed.$$ From the speed you can calculate the centripetal acceleration.$$ From the centripetal acceleration you can calculate the tension.