You cannot get bulk concentration by EDX. However you can get an idea of relative concentration by varying the voltage, the higher is the voltage, the higher is the penetration. So if you perform measurements at different voltages you can see some variations, but it is not really the bulk analysis. 

No. Some elements and molecules rapidly diffuse to the surface at room temperature. See

https://www.researchgate.net/publication/248305890_The_diffusion_of_gold_through_polycrystalline_silver_in_thin_films_at_temperatures_near_150C

Article The diffusion of gold through polycrystalline silver in thin...

What would be your definition of "surface"? Just the terminating atomic layer? 2 layers, 5 layers, 1 nm, 10 nm?

Depending on such a definition, you will classify SEM-EDX as surface specific or not. In my view, it is rather not. [There was a recent thread here on RG discussing this topic].

So, without performing an intelligent set of different methods or using a combination of techniques and/or approachesit will in general be difficult to determine a bulk composition from such experiments. This would probably involve careful calibration of your instrument using suitable standards of known composition before proceeding to determining an unknown sample. Still, also a careful assessment of error margins is in place.

You can get the rough value of bulk concentration by using SEM-EDX analysis. While doing please increase the electric field for penetration of electron.

You can use EDAX.

Depending on EDAX conditions (sample, voltage), you measure different thicknesses. Actually you measure an average concentration of a top "half-sphere" below your electron beam, with a radius of about a micrometer(s). In surface science we call surface concentration of the top 1 nm or even the top mono-layer. So, what you measure by EDAX is rather the bulk concentration. Please, let me know ([email protected]), if you are interested in how to calculate the surface concentration from here.