BDPT - How to handle deterministic ray PDF?
Sorry about leaving it for so long but I was so busy implementing the goddamn algorithm, I forgot about this :)

So after reading up on Veach's thesis pretty closely, I understood what was going on. First of all Veach's thesis describes about BDPT using MIS. However I implemented without MIS using the techniques described in the original Lafortune's paper.

One thing to note is, that we have to calculate the radiance by the light path inversely as opposed to the normal flow in the eye path. As lightxbulb said for point 1, there is no pdf since the step is deterministic. However the deterministic step needs to be multiplied by the Geometric factor, the BRDF evaluation of light vertex to eye vertex and the BRDF evaluation of eye vertex to light vertex.

For the second point, you don't have to worry about NEE since at each eye path vertex there is a path that connects to the light vertex directly, according to PBRT and the paper we can discard the already generated light source and use explicit light sampling there. Calculating the light path radiance separately (as done in light tracing) handles all the respective PDFs for generating the vertices there.

Will post another question regarding the result comparison soon.