Measuring quantum mechanics changes the answer and energy?

Even if you know the initial direction of the particle, this does not tell you which slit the particle will go through. The wavefunction (probability wave) of the particle will still follow the Schrodinger equation. For example, the initial condition in solving the Shrodinger equation could be a Gaussian wave packet in space centered at the measured starting position with some standard deviation determined by the device measuring the initial position. The Gaussian will also be determined by the measured momentum (with some magnitude and direction, each with their own associated uncertainty). This wavefunction will then evolve according to the Schrodinger equation.

Getting to the heart of your question: just because we know the initial position and direction of the particle does not mean it follows a well defined trajectory afterwards. This is just not the case according to basic interpretations of quantum mechanics.

There is only interference if the setup is such that it is not possible to determine through which slit the electron went.