Pretty much all your questions are answered in this guide:

• Film Shooters Collective: A Practical Guide to Using Film Characteristic Curves

What does 0.0 value represents (how to interpret it)?

This is represented as a log scale, so 0.0 passes a certain value of light, 1.0 passes 1/10 that amount of light, 2.0 passes 1/100 that amount of light, and so on. So the density gives somewhat of a dynamic range / contrast ratio. 0.0 would presumably represent 100% light transmitted, ie perfectly transparent area of film.

Obviously with slide film like the Velvia, the density is at its greatest in the blacks (left hand side of exposure) because that's where it blocks the most light, so the density relates to the blackest parts of the image. On negative film the density increases to the right instead for the film.

How do I convert log H to EV?

Convert log lux seconds to EV (absolute - for a given ISO):

ΔEV = log2 [10 x Log Lux Seconds – log10(10/ISO)]

Or just convert a change (delta) in lux seconds (ΔLog Lux Seconds)

ΔEV = log2 (10 x ΔLog Lux Seconds)   

Source: the guide I linked above.

Am I correct that "the best" exposure would be to map average gray point (18% reflected) to (3.0D - 05D) / 2 = 1.25D density? I.e. to the very middle of the linear part on Y axis?

Obviously how to expose is a choice to make, but it makes sense to try and fit as many of the lightest and darkest parts of the scene into the linear part of the curve to represent them accurately.

In the general sense average grey (18% card) mapped to, say, the density of the mid part of the most linear part of the curve, like you suggest, seems to make sense.