Is corporate tax an argument in equal income tax (from labour and capital) debate and does the return on capital depend on rate of the corporate tax? In our country we have 25% personal income tax on labour, 15% corporate tax on corporations and 10% personal income tax on income from capital (e.g. dividends). Pundits in our country are saying that we have flat tax rate across all types of income, because - they are saying - 15% corporate tax and 10% capital income tax amounts to the 25% tax on the income from the capital. Are their analysis correct?

This question leads to the following question - does return in capital (after taxes) depneds on the corporate tax rate? What empirical analysis and models are saying about this? From the one hand - it seems that corporate tax have impact on the gains after corporate tax from the other hand - maybe free market reprices the capital in such manner that the return on capital (after corporate tax) does not depend on the corporate tax rate?

Does the tax system of our country is just, normal, appropriate and similar to for the developed Western democracy country?

I feel that to speak about flat (equal) taxation we should have 25% tax on all the types of income and we should not take into account the corporate tax when considering personal income tax. How this analysis proceeds in Western democracies?

Or should we speak about price/earning share ratio as the most sensible measure of return on capital - does this ratio depend on the corporate tax?
There are too many questions in your post, and I advise to edit out most of them, especially those that are not answerable (like "is the system just" etc).  

For just the first question the answer is No, you don't have the same tax rate on income from labor and from capital.  

Let $\pi$ be profits before tax, $\tau_{\pi}$ the tax rate on profits, $\tau_d$ that tax rate on dividends. Then capital owners will receive (as a percentage of profits)  

$$(1-\tau_d)(1-\tau_{\pi}) =  1-\tau_d-\tau_{\pi}+\tau_d\tau_{\pi}$$

since the dividend tax is applied to profits after tax. So the total tax rate on capital is

$$\tau_c = \tau_d+\tau_{\pi}-\tau_d\tau_{\pi}$$

In your case $\tau_d\tau_{\pi} = 0.10\times 0.15 = 0.015$

So $\tau_c = 0.235$ while tax on labor income is $0.25$. This, in general, is not considered a negligible difference.