Does the necessary delta v given to a satellite (earth orbiting) by the rocket during its launch depend on the positions of other planets? Please justify your answer.
Not really. Here's the effect that a few major bodies would have, depending on the direction launched, expressed in the unit of Newtons/kg. Note that 9.8 N/kg is the equivalent of Earth's gravity. I used this calculator, and this table.
Sun 0.00593 Moon 5.554E-9 Jupiter 1.352E-7 to 3.664E-7
Bottom line, it might be beneficial to launch at noon, but there won't be much of a difference really no matter what you do. These are extremely small, and really just don't make much of a difference. 0.1% of the Earth's gravity at the surface is negligible. Put another way, Earth's gravity at sea level is about 9.8201024640745, 1km higher is 9.8170204389969, for a difference of 0.0030820250776. That's about half of the effect of the sun, a very small effect indeed.
The requirements change considerably if you plan on leaving Earth Orbit, but I won't get too much in to that complexity.