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?
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.