the type of movement in electron jump between levels? what's the type of movement when the electron jump from level to another when gaining or losing a quantum of energy is it actually jump or move in a specific movement?
 A: Not only don't they "move" (as per BillyKalfus's answer), they don't even "jump". And jump's the far more common misconception (also as per Billy's answer:). Here's what more precisely happens...
Consider two states, (a) an initial state $\left|\alpha\right>$ where the electron, if measured, will definitely (with probability $1.0$) be found in a lower-energy state, and (b) a final state $\left|\beta\right>$ where the electron, if measured, will definitely (with probability $1.0$) be found in a higher-energy state.
Now, by "jump" you mean to suggest that there's some time $t_0$ such that the electron's state is $\left|\psi\right>=\left\{{\left|\alpha\right>,\;  t<t_0\atop \left|\beta\right>,\; t>t_0}\right.$. That is, the electron's state discontinuously jumps from $\left|\alpha\right>$ to $\left|\beta\right>$ at time $t_0$.
But that's not what happens. Instead, $\left|\psi\right>$ is some smooth function of time that continuously evolves from $\left|\alpha\right>$ to $\left|\beta\right>$. That is, $\left|\psi(t)\right>=f(t)\left|\alpha\right>+(1-f(t))\left|\beta\right>$, for some $f(t)=\left\{{1.0,\; t<<t_0\atop 0.0,\; t>>t_0}\right.$ that smoothly goes from $1.0$ to $0.0$. So a measurement at an early time will more likely find the electron in state $\left|\alpha\right>$, and at a later time will more likely find it in state $\left|\beta\right>$.
Note that the the electron is never measured in some intermediate-energy state. It's always measured either low-energy or high-energy, nothing in-between. But the probability of measuring low-or-high slowly and continuously varies from one to the other. So you can't say there's some particular time at which a "jump" occurs. There is no "jump".
A: Good question. The atom emits a line spectrum, light in narrow ranges of frequencies. So the source must be an oscillator that is going through millions of oscillations.
One can regard the atom in transition as being in a superposition of the initial and the final stationary states (for an expression, see the answer by John Forkosh). The charge density of such a state is not stationary, see for example this animated gif of the density of a particle in a box: https://commons.wikimedia.org/wiki/File:Particle_in_a_box_(time_evolution).gif
So it will radiate energy with a frequency given by the energy difference between the two states. The contribution of the excited state to the wave function will diminish exponentially: a damped harmonic oscillator. 
A: The electrons don't "move" in the sense that you are probably thinking. They are instantaneously in one state or another. The transition is called a quantum leap and occurs instantly.
